Question

i have a question i know how o solve but i was wonder how to first split it apart or if i would at all... *please dont give answer* .... √72x^3

Answer 1

would i make it √36x^2 times √36x? or would i make it √73 times √x^2 times √x?

Answer 2

√72 times √x^2 times √x*********** sorry

Answer 3

Is that \[\sqrt{72x^3}\]
?

Answer 4

Or just \[\sqrt{72}x^3\]

Answer 5

yes, the exponent inside the square root

Answer 6

Alright, so you need to find out what factors of 72 are perfect squares and then remove those. The same for the variable.

I usually do it like this:

Answer 7

im sorry, but i am confused about your work in the picture

Answer 8

You also know that \[x^3 = x * x * x\]
right?

So, re-writing your expression so you can more easily see what to remove:

\[\sqrt{x * x * x * 2 * 2 * 2 * 3 * 3} = \sqrt{x^2 * x * 2^2 * 2 * 3^2}\]

Answer 9

Regarding my work, I just kept diving 72 by a prime number (2) over and over until I couldn't anymore (without getting a decimal answer). I saw that 9 was divisible by the prime factor 3, giving me 3, which is a prime factor, thus, no more division necessary.

Prime factorization: http://www.mathsisfun.com/prime-factorization.html

Answer 10

thank you!

Answer 11

You're welcome. :)