Question

sqrt16a^7? Simplified using Greatest Perfect Square?

Answer 1

Hey there Liz!
Ok so we have:
\[\large \sqrt{16a^7}\]

16 is a perfect square right? If we want to, we can rewrite our expression like this, and deal with the variable term later:\[\large \sqrt{16}\cdot \sqrt{a^7}\]What is the square root of 16? Do you remember? :)

Answer 2

its 8 right?

Answer 3

no wait 4

Answer 4

Yess good, so that gives us:\[\large 4\sqrt{a^7}\]

Answer 5

To deal with the variable portion.. .hmm let's see.
To take the square root, we divide the `exponent` by 2.

So we want the `largest even power` on a, then we can take it's root.

\[\large 4 \sqrt{a^6\cdot a}\]Understand what I did there? :O a^7=a^6 times a

Answer 6

You took 1 away from the 7 to make it an even number?

Answer 7

yah :) so from here, we can take the square root of the even powered term by dividing the power by 2.

\[\large 4 \sqrt{a^6\cdot a} \qquad=\qquad 4 \sqrt{a^6}\cdot \sqrt{a}\]

Answer 8

What does that give you? :D

Answer 9

4sqrt a^3?

Answer 10

Ok so you divided the exponent by 2, good!
But what that does is, it get's RID OF the square root.

Dividing our exponent by 2 got rid of it.\[\large 4 \sqrt{a^6}\cdot \sqrt{a}\qquad=\qquad 4 a^3\cdot \sqrt{a}\]

Answer 11

So thats the answer? 4a^3*sqrt a?

Answer 12

yessss, good job team!

Answer 13

Thank you so much! :)