Question

Simplify the expression √32+√8−√2
1.)√4•4•2+√4•2−√2
2.)2•2√2+2√2−√2
For the second part where are these numbers coming from. This is from my math class,so the info is correct. I just don't understand how the teacher got these numbers. It just has the numbers not any explanation.

Answer 1

Well we start with

\[\large \sqrt{32} + \sqrt{8} - \sqrt{2}\]

think, how else can you write 32?

the teacher has pointed out that you can write 32 as the product of 4 times 4 times 2

and the square root of 8....you can write 8 as the product of 4 times 2

so we would have

\[\large \sqrt{4\times 4\times 2} + \sqrt{4\times 2} - \sqrt{2}\]

Answer 2

Right

Answer 3

now what has THAT accomplished? all we did was write more numbers

but what is different about some of these numbers?

Hint...what is the square root of 4?

Answer 4

2

Answer 5

right...so we can simplify

Focus on the first square root part here

\[\large \sqrt{4\times 4\times 2}\]

we can also write this *since it is multiplication inside* as

\[\large \sqrt{4} \times \sqrt{4} \times \sqrt{2}\]

right?

so since we know the square root of = 2 we have

\[\large 2 \times 2 \times \sqrt{2}\]
or
\[\large 4\sqrt{2}\] right?

Answer 6

Yes

Answer 7

And using that same logic we know

\[\large \sqrt{4 \times 2} \rightarrow \sqrt{4}\times \sqrt{2} \rightarrow 2\sqrt{2}\]

Answer 8

Thank you @johnweldon1993

Answer 9

No problem!