Question

square root of x^6/y^2

Answer 1

Hint

sqrt(x^n) = x^(n/2)

Answer 2

do you times y^2 on top and bottom ??? to make the bottom perfect

Answer 3

well first tell me what sqrt(x^6) is and what sqrt(y^2) is

Answer 4

not really sure i really get confused when you do the square roots of variables

Answer 5

for example

sqrt(x^8) = x^(8/2) = x^4

Answer 6

Remember, the square root of something is just a quantity that when multiplied by itself gives you the first thing. x*x= x^2, so x is the square root of x^2.

Answer 7

so the square root of x^6 is = x^3 and for y^2=it is y rightttt

Answer 8

Yes!

Answer 9

Note that you didn't really need to know the value

Answer 10

so is the answer just x^3/y

Answer 11

Yes, that's correct if the problem was\[\sqrt{\frac{x^6}{y^2}}\] and we also assume that \(x>0, y>0\)

Answer 12

ok thanks so practically when you have a variable to the power of something divide it by 2 right

Answer 13

Yes, that's what Jim told you with his first post. To take the square root of something is equivalent to dividing its exponent in half. So, \(10^2 = 100\), and \(\sqrt{100} = 10\) because \(10*10 = 100\). If we divide the exponent in half, that gives us \(10^{2/2} = 10^1 = 10\). Same answer, different route.

Answer 14

We can think of it slightly differently: if we have some expression \(x^n\) and want to take its square root, we're trying to find some new exponent \(m\) so that \(x^m*x^m = x^n\). But when we multiply exponentials like that, we just add the exponents, so we know that \(m+m=n\) and that means that \(n = m/2\).

Answer 15

Sorry, \(m = n/2\)