What’s the result? - Simplify fractions with square roots

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  • Опубликовано: 23 дек 2024

Комментарии • 72

  • @MathQueenSusanne
    @MathQueenSusanne  23 дня назад +10

    Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!

  • @bonilsson6349
    @bonilsson6349 8 дней назад +2

    I always get in a good mood when this excellent teacher gives a lesson 😀

  • @fr57ujf
    @fr57ujf 18 дней назад +4

    Very nice explanation. Many other math problem videos I have seen are tediously long. You did it just right.

  • @roland3et
    @roland3et Месяц назад +9

    Nice!
    I like both, the math and the well-structured explanation in fluent English 😊
    🙂👻

  • @grinpick
    @grinpick Месяц назад +4

    Rigorously (and nicely) presented. I note from comments that some others start by "rationalizing the denominator," as I did. In other words, multiply by sqrt10/sqrt10. It gets you to the desired result, just as your approach did. My wife says I'm always rationalizing.

    • @Shay-q8u
      @Shay-q8u 24 дня назад +1

      yes but more complicated and prone to mistakes. Hopefully the student is alert enough to see it is a fraction divided by a fraction then proceed from there.

  • @kareolaussen819
    @kareolaussen819 Месяц назад +16

    Put everything on a common denominator: Big fraction = (√5*√5 +√8•√8)/(√8•√5•√10) = (5+8)/√400 = 13/20.

    • @evgenyzak2035
      @evgenyzak2035 7 дней назад

      That’s how it is supposed to be solved.

  • @HassanLakiss
    @HassanLakiss Месяц назад +2

    Thank you for a nice question and a clear explanation. With respect, I would consider multiplying the top and bottom by √10, resulting in √(50/8) + √(80/5) = √(25/4) + √16 = 5/2 + 4 at the top and each to be divided by 10, resulting in 5/20+4/10.
    (That’s 1/4 + 4/10= 25% + 40%= 65% = 0.65 or 13/20. Just for discussion). Thank you

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs 27 дней назад +4

    There’s a rule called no square roots in denominator if there’s a square root in denominator you can undo it by multiplying the numerator and denominator. Another thing all fractions can be simplified to decimals.

    • @arkadeusz91
      @arkadeusz91 11 дней назад

      There is no such "rule"... it is a common practice because it looks nicer and usually easier to work with further if necessary but it certainly is not a rule. Also not all fractions can be simplified to decimals, as fraction can be irrational and that can at best be approximated to a decimal but is not acceptable as simplified form.

    • @Astrobrant2
      @Astrobrant2 7 дней назад

      It's not always good to convert fractions to decimals. Very often, fractions can cancel out. People who rely heavily on calculators will want to convert, but that often involves more work than just sticking with fractions.

  • @tremoore9831
    @tremoore9831 Месяц назад +3

    For me, the tricky part is remembering all the rules. What's the best way to remember when a rule should or shouldn't be applied?

    • @MathQueenSusanne
      @MathQueenSusanne  29 дней назад +2

      Unfortunately, it just takes practice, but you can do it! I hope my videos help you over time 😉

    • @bonilsson6349
      @bonilsson6349 8 дней назад +1

      PRACTICE PRACTICE PRACTICE 😁

  • @bobs1224
    @bobs1224 14 дней назад +1

    If you don't want to mess with fractions, simply multiply top and bottom by square root of 40 to get (8 + 5)/20.

  • @brando3023
    @brando3023 7 дней назад

    Great 👍 👌

  • @m.h.6470
    @m.h.6470 Месяц назад +2

    Solution:
    √(5/8) = √5/√8 = (√5 * √5) / (√8 * √5) = 5 / √(8 * 5) = 5 / √40
    √(8/5) = √8/√5 = (√8 * √8) / (√5 * √8) = 8 / √(5 * 8) = 8 / √40
    So the Numerator of the whole term is 5/√40 + 8/√40 = 13/√40
    This means the entire term can be rearranged to:
    13 / (√40 * √10)
    = 13 / √400
    = 13/20

    • @GetMatheFit
      @GetMatheFit Месяц назад +1

      You are my hero. I love your solutions.
      Deutsche Susi oder englische Susi deine Kommentare sind immer mega useful.
      LG Gerald

  • @mychaelsmith6874
    @mychaelsmith6874 7 дней назад

    If you square the expression, you get 169/400. The thing you learn from this is that (√(a/b)+√(b/a))^2=(a+b)^2/(ab). Pretty cool.

  • @joseph_donovan
    @joseph_donovan 13 дней назад

    I don't know why most people have a mortal fear and dread of square roots. I went on a blind date once with a colleague from work and while we were waiting for the desert to be served, I waxed lyrical about the beauty and power of square roots. My lady date excused herself and repaired to the ladies ablution room to refresh her facade and never returned!
    The waiter, a po-faced chap who would have not looked out of place as an embalmer at an undertaker's, came to inform that my date had done a runner through the fire escape exit and the bill needed paying.
    I was bereft, broken and beyond all consolation. Was I dejected? No. Was I despondent? No. Was I disappointed? A little.
    My date ran off with a waiter in tight trousers some months later and ended up running a hacienda and donkey sanctuary in Italy.
    I need a hug or some more questions like these gems from Math Queen. Thank you!

  • @Shay-q8u
    @Shay-q8u Месяц назад +2

    love how you made that divide by 10 a multiplication problem. That is exactly why PEMDAS should really be PEMA. Apply the dividing by fractions rule to get rid of division then understand the rules x - y is the same as -y + x and -x - y is the same as -y + -x and that gives you PEMA which IMO eliminates the controversy with PEMDAS and which comes first between multiplication and division.
    oh and if you love mnemonic's, then instead of Please Excuse My Dear Aunt Sally, you instead say Please Excuse My Attitude. (My students get a kick out of that one)

  • @TheEulerID
    @TheEulerID Месяц назад +2

    I just found it easier to multiply top and bottom the square root of 10. Then you get (5/2 + 4) /10. Multiply top and bottom by 2 to get 13/20.

  • @chrgosselin
    @chrgosselin Месяц назад +3

    Thanks for the fun and instructive videos! What’s the name of the app you’re using?

  • @jimmyh1139
    @jimmyh1139 Месяц назад +2

    This is a trivial problem to solve if you start by just squaring the entire fraction to get rid of the radicals, and then take the square root of the result.

    • @ddichny
      @ddichny Месяц назад

      It's not trivial to (correctly) square the numerator.

    • @jimmyh1139
      @jimmyh1139 29 дней назад

      @ddichny Which part of squaring the numerator do you think is not trivial?

  • @jimjackson4256
    @jimjackson4256 24 дня назад

    You are the math queen.

  • @oldjoec3710
    @oldjoec3710 24 дня назад

    I recently found in another RUclips puzzle that the square of x + 1/x for any x is x^2 + 1/x^2 + 2. That pattern jumped out for this numerator. Square of the whole fraction is (5/8 + 8/5 + 2)/10 = ((25 + 64 + 80)/40)/10 = 169/400. --> SQRT(169/400) = 13/20. (This is a variation on kareolausen819's solution, but without all the confusing square roots.)

  • @bigdog3628
    @bigdog3628 Месяц назад +1

    Lets make this a bit cleaner by turning the division into multiplication and since I am using a computer I will write the square root in exponent form which is 1/2 in this case
    (5/8 * 1/10) ^ 1/2 + (8/5 * 1/10) ^ 1/2
    5/80 can simplify to 1/16 and 8/50 can to 4/25
    so we now have
    (1/16) ^ 1/2 + (4/25) ^ 1/2
    square root of 1 is 1 and square root of 16 is 4 so that is 1/4
    square root of 4 is 2 and the square root of 25 is 5 so that is 2/5
    2/5 + 1/4 has the common denominator of 20
    2 * 4 over 5 * 4 is 8/20
    1 * 5 over 4 * 5 is 5/20
    5/20 + 8/20 is 13/20
    No variable to prove and all work is shown so the final Answer is 13/20

  • @michaeldakin1474
    @michaeldakin1474 12 дней назад

    (Sqrt(5)/sqrt(8) + sqrt(8)/sqrt(5)) / sqrt(10)
    (5/sqrt(40) + 8/sqrt(40)) / sqrt(10)
    (13/sqrt(40)) * (1/sqrt(10))
    13/sqrt(400)
    13/20

  • @tomquail6959
    @tomquail6959 Месяц назад +4

    Thank you. Very clear.

  • @leonardpoindexter5289
    @leonardpoindexter5289 Месяц назад +1

    How sad , I'm watching this on a Saturday night. Still very much interesting. Thanks

    • @MathQueenSusanne
      @MathQueenSusanne  Месяц назад +1

      I get why it might feel that way, but honestly, choosing to learn something new is a great use of time. That’s way more productive than most Saturday nights. 😉 I’m glad you found it interesting-thanks for watching!

    • @user-lu6yg3vk9z
      @user-lu6yg3vk9z 20 дней назад

      @@MathQueenSusanneu do tutoring ?

  • @se7sTC
    @se7sTC 16 дней назад

    Got the same result by squaring the fraction, simplify to 169/400 then take the square root of that

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs 27 дней назад +1

    (Sqrt[5/8]+Sqrt[8/5])/Sqrt[10]=0.65=13/20 final answer You find Square roots of fractions by separating them.

  • @yurenchu
    @yurenchu Месяц назад +1

    ( √(5/8) + √(8/5) ) / √10 =
    ... Note: 5/8 = 40/64 , 8/5 = 40/25 ...
    = ( √(40/64) + √(40/25) ) / √10
    = ( (√40)/8 + (√40)/5 ) / √10
    = ( 1/8 + 1/5 )*(√40) / √10
    = ( 5/40 + 8/40 )*(√40) / √10
    = ( 13/40 )*(√40) / √10
    = ( 13/40 )* √(40/10)
    = ( 13/40 )* √(4)
    = ( 13/40 )* 2
    = 13/20
    = 0.65

  • @frankjowitt7323
    @frankjowitt7323 Месяц назад +3

    How about just mult numerator and denominator by sqrt 40?
    Simpler.

    • @timeonly1401
      @timeonly1401 Месяц назад

      Yes, this clears all the fractions within the fractions. And, in this problem, happens to clear ALL the radicals, too!
      Numerator:
      N = √40 [ √(8/5) + √(5/8) ]
      = √[40(8/5)] + √[40(5/8)]
      = √(8*8) + √(5*5)
      = 8 + 5
      = 13
      Denominator:
      D = √40 √10
      = √(40*10)
      = √400
      = 20
      So, N/D = 13/20
      or, = 0.65

    • @PhilipTa10
      @PhilipTa10 Месяц назад

      Yeah, also what I did

    • @adamoksiuta4715
      @adamoksiuta4715 Месяц назад

      You can multiply numerator and denominator by sqrt of 10, it is enough.

  • @mijoizagas3747
    @mijoizagas3747 20 дней назад

    Awesome ❤

  • @MrImoT
    @MrImoT 7 дней назад

    Amazing... :)

  • @alansun70
    @alansun70 Месяц назад +2

    This looks tricky. It's a complex fraction. You'd start by simplifying the numerator.

  • @Birol731
    @Birol731 Месяц назад +1

    My way of solution ▶
    [√5/8 + √8/5 ]/ √10
    = [(√5/√8 + √8/√5] /√10
    = (√5*√5 + √8*√8)/√5*√8] : √2*√5
    = [(5+8)/√5*√2²2] : √2*√5
    = [13/√5*2√2] : √2*√5
    = 13/√5*2√2*√2*√5
    = 13/(5*2*2)
    = 13/20 ✅
    or
    = 0,65

    • @m.h.6470
      @m.h.6470 Месяц назад

      you forgot the opening bracket AND a full bracket in the denominator on the line
      = (√5*√5 + √8*√8)/√5*√8] : √2*√5
      it should be
      = [(√5*√5 + √8*√8)/(√5*√8)] : √2*√5
      The subsequent lines are also missing the same full bracket. Otherwise the calculation result would be VERY different.

  • @KrytenKoro
    @KrytenKoro Месяц назад +1

    {25}+{64}/{400}=5+8/20=13/20

  • @billheyn9363
    @billheyn9363 6 дней назад

    Faster to multiply by square root of 40 both numerator and denominator.

  • @thomasolson7447
    @thomasolson7447 Месяц назад +1

    Well... I noticed a pattern with Fibonacci Numbers. It's not what you did. It's a little different. I guess I can say it is derived from this question.
    f:=n-> (((1+sqrt(5))/2)^n-((1-sqrt(5))/2)^n)/sqrt(5)
    (sqrt(f(n)/f(n + 1)) + sqrt(f(n + 1)/f(n)))/sqrt(f(n)*f(n + 1)) = f(n+2)/(f(n)*f(n+1))
    And it works in non-integer values. Which is even cooler.
    * Oh, I see it now. I'll just leave it the way it is. Let you all figure it out.

  • @ghlscitel6714
    @ghlscitel6714 18 дней назад

    Got 13/20 with a shorter path, all by heart

  • @evgenyzak2035
    @evgenyzak2035 7 дней назад

    It’s easier to work upstairs first, then ten comes at the end.

  • @reisegeschmackcom8388
    @reisegeschmackcom8388 Месяц назад +1

    ❤️🚀

  • @borisjeud8464
    @borisjeud8464 17 дней назад

    13
    ----
    2
    ---
    10

  • @jeffbuxton4644
    @jeffbuxton4644 23 дня назад

    I did it the hard way and got (2.5+4)/10= 0.65

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs 27 дней назад +1

    13/2=6.5 so 13/20=0.65

  • @spdas5942
    @spdas5942 29 дней назад

    13/20 in no sec

  • @utedalheimer1742
    @utedalheimer1742 Месяц назад +1

    ❤ Dankeschön ❤

  • @alexmarkov9918
    @alexmarkov9918 24 дня назад

    Square it and get nice simplifications

  • @dionysus2006
    @dionysus2006 20 дней назад

    My XL spreadsheet says 0.65. We have tools, use them

  • @gheffz
    @gheffz 19 дней назад

    🙃

  • @rolansmith9951
    @rolansmith9951 2 дня назад

    Someone needs a date 😂

  • @BryanM362
    @BryanM362 19 дней назад

    Love a smart, bubbly, beautiful woman!

  • @MD-kv9zo
    @MD-kv9zo Месяц назад +2

    .65? Pre video

  • @estatehelper921
    @estatehelper921 Месяц назад +1

    красотка, целую в щечки.

  • @audreydaleski1067
    @audreydaleski1067 25 дней назад

    No.

  • @audreydaleski1067
    @audreydaleski1067 25 дней назад

    Too easy. A couple ways to solve.