Question

Simplify
4sqrt180

Answer 1

\[4\sqrt{180}\]

Answer 2

Factor 180 to find perfect squares.

Answer 3

i dont rememeber how to do that

Answer 4

Basic process of factoring a number: notice what numbers go into it for sure, then divide those out, then repeat with what you get. So with 180 for example, you know for sure that it's divisible by 2 because it's even, right? So divide it by 2 and you get \(2\cdot90\). So then repeat with 90, you know that's divisible by 2 again, so you get \(2\cdot2\cdot45\). Now 45 you know is divisible by 5 because it ends in 5, so you get \(2\cdot2\cdot5\cdot9\). And 9 is just 3 times 3, so your final factorization is \(2\cdot2\cdot3\cdot3\cdot5\). That's the same as \(2^2\cdot3^2\cdot5\), so now you can pull those perfect squares out and square root them.

Answer 5

and after that ?

Answer 6

That's it. You have \(4\sqrt{180}=4\sqrt{2^2\cdot3^2\cdot5}=4\sqrt{2^2}\sqrt{3^2}\sqrt{5}=4\cdot2\cdot3\sqrt{5}=24\sqrt{5}.\)

Answer 7

thanks i get it