Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers.

Question

√6x3 √18x2

I have never been good at figuring this formula out with square roots and I am practicing for a test next week and I really want to graduate so if you can show me how to do the steps to this problem. Please and Thank you

Answer 1

You must know the first few perfect squares, such as
4, 9, 16, 25,... perhaps up to 144
so for √(any number) , attempt to split the number into factors containing one or more of those perfect squares.
e.g. √18 = √9 √2 = 3√2
√35 = √5√7 , nothing gained because neither 5 nor 7 is a perfect square.

If you have large numbers under the square root, such as
√1344
factor 1344 and hope to find a perfect square
e.g.
1344 = 4x336
= 4x4x84
= 4x4x4x21
= 64x21
So √1344 = √64√21 = 8√21

if you have √'s of variable powers, break them up into even exponent roots
remember √x^ = x
√x^4 = x^2
√x^6 = x^3 etc

e.g. √x^13
= √x^12 √x
= x^6 √x

Your last problem:
√18x2
= √9√2√x^2
= (3)(√2)(x)
= 3x√2