[3√20 + 7√5] / [√2 x √3] [3√(4 x 5) + 7√5] / [√6] [3 x 2√( 5) + 7√5] / [√6] [6√( 5) + 7√5] / [√6] [13√ 5] / [√6] ---> Rationalizing the Denominator by multiplying both numerator/denominator with √6 To preserve the ratio of the expression [√6][13√ 5] / [√6][√6] [13√30] / 6 --->ANS
Super simple: (When you have fraction exponents the numerator is the power and the denominator is the root.) Numerator: 3(20^1/2) + 7(5^1/2) 3(4^1/2 * 5^1/2) + 7(5^1/2) 6(5 ^ 1/2) + 7(5^1/2) 13(5^1/2) Denominator: (2^1/2) * (3^1/2) 6^1/2 We can NOT have a radical in the denominator so we must get rid of sqr of 6 by finding the next multiple of it that is a perfect square 6^1/2 * 6^1/2 36^1/2 or just 6 Since we multiplied the denominator by 6^1/2 me must also multiply the numerator by 6^1/2 13(5^1/2 * 6^1/2) 13(30^1/2) Final answer is [13(30^1/2)] as nothing can be simplified further.
@@bigdog3628 Of course we can have radicals in denominators. They're just numbers. It's fine. Nobody outside of mindless dogmatic schoolteachers gives a toss. The entire mathematical world is absolutely fine with, for example, the sine and cosine of 45 degrees being 1/√2. It's completely normal.
@@chrisdissanayake6979 That's a good thing to forget because it's incorrect. We can have a square root in the denominator. It's normal and completely fine. This guy's obsession with it has no mathematical basis whatsoever. But if you prefer to follow his style then rationalising the denominator is obviously fine too.
√20 = √(4×5) = √4 × √5 = 2√5 So the numerator is 6√5 + 7√5 = 13√5 The denominator is √2 × √3 = √(2×3) = √6 So the whole expression simplifies to 13√5 / √6 = 13√(⅚) Contrary to the nonsense in the video, √6 in the denominator is absolutely fine. Mathematics has no problem with irratuonal numbers in denominators. It's normal. But if you prefer to rationalise the denominator then just multiply by √6 / √6 to get (13√5 × √6) / (√6 × √6) 13√30 / 6 AND FOR CHRIST'S SAKE STOP EXPLAINING √6 × √6 = 6 LIKE THAT!!! This has got to be one of your absolute STUPIDEST repetitive mistakes. √6 × √6 = 6 because that's the DEFINITION of a square root. It doesn't need any more explanation of that. The only reason someone wouldn't already know that √6 × √6 = 6 is if they don't know what a square root is. Why would you not explain to them what a square root is? In a video that's all about square roots, you're happy for people to get to the end and still not understand this basic point!
[3√20 + 7√5] / [√2 x √3]
[3√(4 x 5) + 7√5] / [√6]
[3 x 2√( 5) + 7√5] / [√6]
[6√( 5) + 7√5] / [√6]
[13√ 5] / [√6] ---> Rationalizing the Denominator by multiplying both numerator/denominator with √6
To preserve the ratio of the expression
[√6][13√ 5] / [√6][√6]
[13√30] / 6 --->ANS
Super simple:
(When you have fraction exponents the numerator is the power and the denominator is the root.)
Numerator:
3(20^1/2) + 7(5^1/2)
3(4^1/2 * 5^1/2) + 7(5^1/2)
6(5 ^ 1/2) + 7(5^1/2)
13(5^1/2)
Denominator:
(2^1/2) * (3^1/2)
6^1/2
We can NOT have a radical in the denominator so we must get rid of sqr of 6 by finding the next multiple of it that is a perfect square
6^1/2 * 6^1/2
36^1/2 or just 6
Since we multiplied the denominator by 6^1/2 me must also multiply the numerator by 6^1/2
13(5^1/2 * 6^1/2)
13(30^1/2)
Final answer is [13(30^1/2)] as nothing can be simplified further.
@@bigdog3628 Of course we can have radicals in denominators. They're just numbers. It's fine.
Nobody outside of mindless dogmatic schoolteachers gives a toss. The entire mathematical world is absolutely fine with, for example, the sine and cosine of 45 degrees being 1/√2. It's completely normal.
Thank you Sir!
I had forgotten that we can’t have a square root as the denominator and we have to rationalize!
🙏🏽
@@chrisdissanayake6979 That's a good thing to forget because it's incorrect.
We can have a square root in the denominator. It's normal and completely fine. This guy's obsession with it has no mathematical basis whatsoever.
But if you prefer to follow his style then rationalising the denominator is obviously fine too.
3V20 + 7V5 / V6 = (3V20 + 7V5) . V6 / V6.V6 = 3V120 + 7V30 / 6
( 120 = 3 . 2 . 2 . 2 . 5 so V120 = 2V30 )
= 3 . 2V30 + 7V30 / 6 = 6V30 + 7V30 / 6 = 13V30 / 6
You are not solving here you are simplifying ; )
👍
1/26 of this video was dedicated to requesting subscriptions. Or, 3.85%, if you prefer.
I ended up with 13 root 30 divided by 6. It was quite complicated.
Respectful should mean calling a JACKASS a JACKASS
I got it.i was little confused at first.
6√5+7√5=13√5 so, we have
13√5/√6 * √6/√6=(13√30)/6
13rt5/6
got (13 sr 30) / 6 just took time as you explained thanks for the fun
13sq.root of 30/6
👀👀
👍👋🙏💪🌎😎
John the JACKASS, you should be ashamed, to make a kindergarten stuff look so difficult
you lost me
√20 = √(4×5) = √4 × √5 = 2√5
So the numerator is
6√5 + 7√5 = 13√5
The denominator is
√2 × √3 = √(2×3) = √6
So the whole expression simplifies to
13√5 / √6 = 13√(⅚)
Contrary to the nonsense in the video, √6 in the denominator is absolutely fine. Mathematics has no problem with irratuonal numbers in denominators. It's normal.
But if you prefer to rationalise the denominator then just multiply by √6 / √6 to get
(13√5 × √6) / (√6 × √6)
13√30 / 6
AND FOR CHRIST'S SAKE STOP EXPLAINING √6 × √6 = 6 LIKE THAT!!!
This has got to be one of your absolute STUPIDEST repetitive mistakes.
√6 × √6 = 6 because that's the DEFINITION of a square root. It doesn't need any more explanation of that.
The only reason someone wouldn't already know that √6 × √6 = 6 is if they don't know what a square root is.
Why would you not explain to them what a square root is? In a video that's all about square roots, you're happy for people to get to the end and still not understand this basic point!
I will agree to disagree with you here.