Question

Simplify each radical expression. Leave in radical form. Show your work.
sqrt 45n^5

Answer 1

\[\sqrt{45n^{5}}\]

to simplify a root, you want to find factors of 45, which one of them must be a square number
you want the largest square number you can get that goes into it

so you know that the largest square number that goes into 45 is 9
9 multiplied by 5 goes into 45

therefore you re write 45 as

\[\sqrt{9 \times 5n^{5}}\]

\[\sqrt{a \times b}=\sqrt{a}\sqrt{b}\]
to get
\[\sqrt{9}\sqrt{5n^{5}}\]