Verified answer

Note that 32 contains the perfect square factor of 16. Then, we have..

3√(16 * 2)

= 3 * 4√2

= 12√2

Hence, 3√32 = 12√2

I hope this helps!

3√32 = 3 * √16 * √2

So --> 3 *4 *√2 = 12√2

√32=√16 . √2

=√4 . √4 . √2

= 2 . 2 . √2

=4 . √2

3. √32 = 3. 4. √2

= 12 . √2

I think this is what you are looking for

let us take this

3√32=12√2

=3√16×2=12√2

=3×4√2=12√2

(since root of 16=4, 4 can be taken outside and multiplied by 3)

=12√2=12√2

3√32

You can factor out all the primes of 32 under the square root.

3√(2*2*2*2*2)

Now, you can separate the square root. You can only do this when everything under the square root is being multiplied.

3√(2*2) * √(2*2) * √2

Now, you multiply under the square roots. 2*2=4

3√4 * √4 * √2

The square root of 4 is 2 because 2 times 2 is 4.

3*2*2*√2

Multiply.

12√2

What you are doing wrong is adding 3, 2, and 2 instead of multiplying them.

I am writing the answer step by step so that you get it.

3√32 is equal to 3√4.4.2

3√4.4.2 is equal to 3.4√2

3.4√2 is equal to 12√2

Simple as it.

3*sqrt 32 = 3*sqrt (16*2)= 3*4*sqrt(2)

they both have no powers