How to solve this problem?

Question

evaluate each expression:
1. 27^1/2 x 20^1/2

I have to solve this without a calculator. So just simplify basically

Answer 1

raised to 1/2 means "find the square root"

so "square root of 27 x square root of 20" (i'll just use check mark for square root)

√27 * √20 = √(27 * 20)
= √ 540

540 is not a perfect square so you can't get a whole number,,
so factor it out,one of which is a perfect square,,
we'll have 36 *15 (36 is the perfect square)

= √540
=√(36 * 15)
so we can find for the root

the answer now is 6 √ 15 (six square root of fifteen)

Answer 2

27^(1/2) * 20^(1/2)
= 540 ^ (1/2) since powers r equal a ^ m* b ^ m = (ab) ^ m
= (9 * 2 * 5 * 2 * 3) ^ (1/2)
= 3 * 2 * (5 * 3) ^ (1/2)
= 6 * 15 ^ (1/2)
now use a logarithm book to find the root and voila u have the answer by multiplying the root of 15 with 6!
U could also find root using long division method!

Answer 3

When you have a number raised to the 1/2 power, it means that you take the square root of that number. If it is to the 1/3 power you would take the cube root, and so on and so fourth.

So for this expression, you take the square root of 27 and multiply it by the square root of 20. You can do this on a calculator, and you will come up with the answer 23.237900077244501311075592398694.

Hope this helps.