√8 = 2√2 ? why?

[yumi2012]

How is this possible?

Then what is √32 = ?

[Bill@VeritasPrep]

Sqrt(8) = Sqrt(4*2)

Sqrt(4*2) = Sqrt(4) * Sqrt(2)

We know what the square root of 4 is: 2.

Thus, the square root of 8 simplifies to 2*sqrt(2)

For the square root of 32:

Sqrt(32) = Sqrt(16*2)

Sqrt(16*2) = Sqrt(16) * Sqrt(2)

4*Sqrt(2)

[alex.gellatly]

How is this possible?

Then what is √32 = ?

You can think of √ as this: You need two prime numbers inside the √ to take out and become one outside the √ sign.
For example:
If you find all the prime numbers in 8 you get 2*2*2=8. So.. √2*2*2= 2√2 because you have 3 2's. You can take two 2's out to become one 2. But because you have 1 left over it must stay inside.

In √32 we get 2*2*2*2*2=32, so we have 5 2's. We can "take out" 4 2's (but remember you take out two becomes one) so... 2*2=4. We still have one left over inside so our answer is 4√2

Hope this helps

[Brent@GMATPrepNow]

All of this uses a rule that says: sqrt(ab) = [sqrt(a)][sqrt(b)]
So, sqrt(32) = sqrt(16 x 2)
= sqrt(16) x sqrt(2)
= 4 x sqrt(2)
= 4sqrt(2)

Cheers,
Brent