Do note that it may be beneficial in some cases to not immediately remove a radical from the denominator. Specifically if you're mulitplying, dividing, or using exponents, it may be simpler to keep those denominators radical until you need to do addition or subtraction or until you come up with your final result, which will generally need to be formatted in a proper format. You'll find this happens quite often when dealing with multiple variables in a series of equations, particularly in fields that deal with a lot of radicals, like geometry.
Hello, Professor! Could we write square root of 1/2 like 2 exponential -2? Would it be solvable? Is your explanation the only way to solve this equation? Thank you in advance.
We really need to stop calling this symbol square root. It is not square rooted is radical, and there is a difference. This becomes confusing to students.
@rodrodrigues5402 The symbol itself is called a radical, or called the “radical.” In other words, the symbol, the radical, and the terms or expressions inside and beneath it are together called “radical notation,” or, to some extent, “radical notation” is called “radicals.” Makes no difference whether it’s the square root, the cube root, the 5th root, the 0.5 root, the 3/4 root….etc., the symbol representing all of them is nonetheless called the “radical,” with the numbers 2, 3, 5, 0.5, 3/4,…..etc. being the “indexes” of the radical symbol. I think it’s called “square root” because its “root(s),” that is, its solution(s) equals the radicand when they’re “squared,” that is, equals the number inside and beneath the radical symbol when those “solutions”, or “roots,” are “squared.” For example, (+\-2)^2 (“squared”) equals the “4” inside and beneath the radical symbol √ 4. The cube root of 9 equals 3, and when 3 is cubed (3 to the 3rd power, 3^3) it equals 9. In other words, the two operations and processes, that is, “square root” and “squared,” are inverses of each other, one gets us back to the other, and vice versa! So that +\-2 are the roots of the √ 4, or the solutions or roots of the square root of 4, √ 4, such that when those roots, those solutions, are “squared” they equal the value “4” that’s inside and beneath the “”square” root” symbol, and the √ 4 equals +\-2. Moreover, the symbol, or, the radical, is called the “square root” because it’s an understood convention that the √ symbol means the square root of a number so as to distinguish it from, say, the cube root or the 5th root of a number, etc, without the “2,” which is called the “index,” being written above the radical symbol in the same manner in which those and other “indexes” are written above the radical symbol. Like with logarithms, log base 10, which is called the “common log,” is written Log x which means log base 10 of x, with the number 10 being the omitted but the understood and agreed upon convention of writing log base 10 expressions. Logs of other bases are represented by writing their bases. log base 3, for example, will be and must be written with the number “3,” its base (dare I call it its “index”), like, log subscript 3 x. In other words, like for log x the 10 isn’t written but understood, the “index” “2” which represents the square root of some number inside and beneath the radical symbol for taking square roots isn’t written but we understand it, similarly, by an agreed upon convention, to be and mean take the square root of a number and therefore in effect to be there. For the cube root of some number, same for all other roots of some number, except the “square root of a number, the “index” “3” is always written above the radical symbol, but for the square root of some number inside and beneath the square root radical symbol the “index” “2” is never written but is always understood to mean the square root of some number. So there’s nothing at all wrong with calling the symbol the “square root”!
An easier and faster method is to use the bowtie method for adding fractions. Cross multiply twice and add the two numbers to create the numerator and multiply the two denominators to create the denominator. Before doing so, change √1/2 to √1/√2 to create the first fraction. The other fraction is √2/1.
I thought I had the answer all set; easy peasy... 2.121320343. But then he said "No calculator!" and, well, he got me there. I would have never come up with any kind of valid answer without a calculator.
Do note that it may be beneficial in some cases to not immediately remove a radical from the denominator. Specifically if you're mulitplying, dividing, or using exponents, it may be simpler to keep those denominators radical until you need to do addition or subtraction or until you come up with your final result, which will generally need to be formatted in a proper format. You'll find this happens quite often when dealing with multiple variables in a series of equations, particularly in fields that deal with a lot of radicals, like geometry.
Year 8 maths, 30 seconds problem.
First, Got to know rationalise the denominator, √(1/2) = 1/(√2) = (√2)/2.
Therefore √2 + √(1/2) = (2√2)/2 + (√2)/2 = (3√2)/2. Easy-peasy
I guess it's improper to have sqrt(2) in denominator???
sqrt(1/2) = (sqrt(1))/(sqrt(2))
= 1/(sqrt(2))
= (sqrt(2))/2
= (1/2)(sqrt(2))
so
(sqrt(2)) + (sqrt(1/2))
=(sqrt(2)) + (1/2)(sqrt(2))
=(3/2)(sqrt(2))
Hello, Professor!
Could we write square root of 1/2 like 2 exponential -2?
Would it be solvable?
Is your explanation the only way to solve this equation?
Thank you in advance.
2^(-2) is ¼ and rewriting it with an exponent won't help
@@Viki13 It could be written as 2^(-1) then 🤔
We really need to stop calling this symbol square root. It is not square rooted is radical, and there is a difference. This becomes confusing to students.
Karl Marx was a radical too. :)
sqrt(Karl Marx) = a r sqrt(Klmx) 🤔
I majored in math. Doesn't bother me.
@rodrodrigues5402
The symbol itself is called a radical, or called the “radical.” In other words, the symbol, the radical, and the terms or expressions inside and beneath it are together called “radical notation,” or, to some extent, “radical notation” is called “radicals.” Makes no difference whether it’s the square root, the cube root, the 5th root, the 0.5 root, the 3/4 root….etc., the symbol representing all of them is nonetheless called the “radical,” with the numbers 2, 3, 5, 0.5, 3/4,…..etc. being the “indexes” of the radical symbol. I think it’s called “square root” because its “root(s),” that is, its solution(s) equals the radicand when they’re “squared,” that is, equals the number inside and beneath the radical symbol when those “solutions”, or “roots,” are “squared.” For example, (+\-2)^2 (“squared”) equals the “4” inside and beneath the radical symbol √ 4. The cube root of 9 equals 3, and when 3 is cubed (3 to the 3rd power, 3^3) it equals 9. In other words, the two operations and processes, that is, “square root” and “squared,” are inverses of each other, one gets us back to the other, and vice versa! So that +\-2 are the roots of the √ 4, or the solutions or roots of the square root of 4, √ 4, such that when those roots, those solutions, are “squared” they equal the value “4” that’s inside and beneath the “”square” root” symbol, and the √ 4 equals +\-2. Moreover, the symbol, or, the radical, is called the “square root” because it’s an understood convention that the √ symbol means the square root of a number so as to distinguish it from, say, the cube root or the 5th root of a number, etc, without the “2,” which is called the “index,” being written above the radical symbol in the same manner in which those and other “indexes” are written above the radical symbol. Like with logarithms, log base 10, which is called the “common log,” is written Log x which means log base 10 of x, with the number 10 being the omitted but the understood and agreed upon convention of writing log base 10 expressions. Logs of other bases are represented by writing their bases. log base 3, for example, will be and must be written with the number “3,” its base (dare I call it its “index”), like, log subscript 3 x. In other words, like for log x the 10 isn’t written but understood, the “index” “2” which represents the square root of some number inside and beneath the radical symbol for taking square roots isn’t written but we understand it, similarly, by an agreed upon convention, to be and mean take the square root of a number and therefore in effect to be there. For the cube root of some number, same for all other roots of some number, except the “square root of a number, the “index” “3” is always written above the radical symbol, but for the square root of some number inside and beneath the square root radical symbol the “index” “2” is never written but is always understood to mean the square root of some number.
So there’s nothing at all wrong with calling the symbol the “square root”!
Still don't understand why the radical symbol is not permitted in the denominator. Allowing such would reduce frequency mistakes.
Same here. Another correct answer is (3)sqrt(1/2) which is equal to (3/2)sqrt(2).
Without calculator, without paper, only delicious brainpower: 2/2 . SQR(2) + SQR(2)/2 = 3/2 . SQR(2)
√2+√1/2=3/2=1 1 (x+1x-1)
Thank you
Don't have time to stay until the end, but in 30 seconds I reckon the answer is about 2.1, made up of approximately 1.4 plus 0.7
This is how I did it to get an actual number instead of turning it into another equation. Give or take 2.1 and change
Multiply by (sqrtof2/sqrtof2) simplifies ? to : 3/sqrtof2
You could use square root tables
to find the answer.I did this when
I was young.
An easier and faster method is to use the bowtie method for adding fractions. Cross multiply twice and add the two numbers to create the numerator and multiply the two denominators to create the denominator. Before doing so, change √1/2 to √1/√2 to create the first fraction. The other fraction is √2/1.
made is so much harder. You write the question mark as 'x' then you square both sides and get the answer very simple.
Square root of 2
Seems easy?! 3 root 2 /2 !! :o
I got 3 ÷ root'2... which I know is 1.414... and 3/1.414 is slightly greater than 2. Say 2.1+
1/sqrt(2) is the same as 1/2*sqrt(2)
so your solution should be correct.
3 root 2 / 2 :)
John the eternal JACKASS special ability, always makes a mountain of a mole hill. This is a 3rd grade problem
Totally lost me and I have had the before…
I thought I had the answer all set; easy peasy... 2.121320343. But then he said "No calculator!" and, well, he got me there. I would have never come up with any kind of valid answer without a calculator.