To solve, I pulled out the greatest common factor, 4.

= sqrt[4((4*5) + (2*8))]
= 2 * sqrt (20+16)
= 2 * sqrt (36)
= 2 * 6
= 12

sqrt[4(4*20 + 2*32)]
= 2*sqrt[80 + 64]
= 2*sqrt[144]
= 2*12
= 24

See where u went wrong? You took an extra 4 out!

Thanks for the reply.

I was thinking that the 4 needed to be distributed. But the question involves multiplication, not addition, so I ended up pulling the 4 out twice.

NextGreatLeader wrote:I understand the answer explanation for this problem, but I don't understand why my method is wrong and why I got a different answer.

Solve:
sqrt[(16)(20) + (8)(32)]

To solve, I pulled out the greatest common factor, 4.

= sqrt[4((4*5) + (2*8))]
= 2 * sqrt (20+16)
= 2 * sqrt (36)
= 2 * 6
= 12

Why is this method wrong?

You have done it wrong in the highlighted step. The correct way is :

sqrt[(16)(20) + (8)(32)]
=>sqrt[(4*4)(4*5) + (4*2)(4*8)]
Now you can take one 4 common or you can take two 4's common. I will first tell you the easy way.

Take two 4's common. Then
sqrt[(4*4)(4*5) + (4*2)(4*8)]
=>sqrt(4*4){sqrt[(4*5) + (2)(8)]}
=>4*{sqrt[20+16]}
=>4*sqrt (36)
=>4*6
=>24

If you take one 4 common (it will involve some extra calculation) then :
sqrt[(4*4)(4*5) + (4*2)(4*8)]
=>sqrt4*sqrt[(4)(4*5) + (2)(4*8)]
=>2*sqrt[(80) + (64)]
=>2*sqrt[(144)]
=>2*12
=>24.

Hope you understood.