Question

Can you simplify the expression?

Answer 1

please apply the distributive property of multiplication over addition

Answer 2

namely:
\[\sqrt{6}*\sqrt{33}+\sqrt{6}*7\]

Answer 3

do you know how to multiply two radical each other?

Answer 4

oops ...two radicals each other?

Answer 5

I'm sorry! I had to feed my nephew. @Michele_Laino I'm not sure...

Answer 6

for example we have:
\[\sqrt{6}*\sqrt{33}=\sqrt{6*33}\]
so please complete

Answer 7

6*33=...

Answer 8

204

Answer 9

6*33=198 do you agree?

Answer 10

Yes.

Answer 11

now note that 198=9*22, do you agree?

Answer 12

Yes, I do.

Answer 13

perfect! So we can write:
\[\sqrt{6}*\sqrt{33}=\sqrt{198}=\sqrt{9*22}=\sqrt{3^{2}*22}\]
do you agree, please?

Answer 14

@Jonnychewy

Answer 15

Sounds good to me. =)

Answer 16

ok! please note that the exponent of 3 is 2, so we can take out it of the root sign,

Answer 17

and we can write:
\[\sqrt{3*22}=3*\sqrt{22}\]
is it right for you?

Answer 18

Yes.

Answer 19

oops sorry:
\[\sqrt{3^{2}*22}=3*\sqrt{22}\]

Answer 20

it has been sufficient divide the exponent of 3^2, by 2

Answer 21

namely 2/2=1 and 1 is the new exponent of 3 when it is out of square root

Answer 22

so your expression is simplified as below:
\[3\sqrt{22}+7\sqrt{6}\]
that's all

Answer 23

Wow! Okay, that's what I was thinking too. Thank you!

Answer 24

Thank you!