Question

Can someone please help me with this?


Which statement is true about the product square root of 2(5 + square root of 8)?

It is rational and equal to 7.
It is rational and equal to 9.
It is irrational and equal to 4 + square root of 10.
It is irrational and equal to 4 + 5square root of 2.

Answer 1

@EclipsedStar

Answer 2

This what it looks like?
\[\large \sqrt{2}*(5+\sqrt{8})\]

Answer 3

yes

Answer 4

do you recall how to distribute that to expand it?

Answer 5

i do not know how to distribute a square root

Answer 6

it is the same as if it was not a square root.

a*(b + c) = a*b + a*c

Answer 7

oh okay so square root of 10 + square root of 16?

Answer 8

Distributing gives this to begin with
\[\large \sqrt{2}*(5+\sqrt{8})=5*\sqrt{2}+\sqrt{8}*\sqrt{2}\]

Answer 9

You cant do anything to simplify the first term , but the second term can be simplified.
rewrite the 8 as 2*4, and the square root of 4 is 2.

\[\sqrt{8}* \sqrt{2}=\sqrt{4*2}*\sqrt{2}=\sqrt{4}\sqrt{2}*\sqrt{2}=2\sqrt{2}*\sqrt{2}=2*2=4\]

Answer 10

so overall the thing simplifies to

\[\large \sqrt{2}*(5+\sqrt{8})=4+5\sqrt{2}\]

Answer 11

oh ok

Answer 12

can you tell me what does rational and irrational mean @DanJS ?

Answer 13

i just want to know for future problems

Answer 14

a number is rational if it can be written as a fraction of whole numbers a/b

Answer 15

if it cant be written as a/b ; then it is irrational

Answer 16

ok thank you so much

Answer 17

square root 2 is irrational... welcome