Question

What is the product of the square root of 2. (6bthe square root of 16. - 2b)?

Answer 1

\[\sqrt{2}(6b \sqrt{16}-2b)\]

Answer 2

Please simplify if possible.

Answer 3

\(\sqrt{16}\) -- You had better tell me if that can be simplified.

Answer 4

4

Answer 5

Got it. Substitute that and tell me what's next.

Answer 6

substitute it as b?

Answer 7

Why would you do that? We have done nothing with 'b'.

Rather than write \(\sqrt{16}\), write 4.

Answer 8

oh ok

Answer 9

\[\sqrt{2}(6b \sqrt{4}-2b)\]

Answer 10

Why is it \(\sqrt{4}\)? \(\sqrt{16} = 4 \ne \sqrt{4}\)

Write it again, with just '4'.

Answer 11

\[\sqrt{2}(6b+4-2b)\]

Answer 12

Why did it turn into "+4". It was multiplied by 6b a moment ago. Rewrite it again without adding anything. Just substitute. Write it EXACTLY as it was originally - with ONE difference. Don't write \(\sqrt{16}\). Write 4 instead.

Answer 13

\[\sqrt{2}(10b -2b)\]

Answer 14

Where did the 6 go? That was NOT an EXACT reproduction. Make an EXACT reproduction. Don't make ANY other change.

What does \(b\sqrt{16}\) mean? Some number b, multiplied by the number \(\sqrt{16}\). If you make a direct substitution, you should get \(b4\), meaning some number b, multiplied by 4. Don't try to do anything with it. JUST SUBSTITUTE. \(\sqrt{16} = 4\)

Answer 15

ok ...

Answer 16

im just confused

Answer 17

No, you must learn to substitute.

\(6b\sqrt{16} = 6b4\)

I agree that's a little awkward-looking. Maybe it would be better if we inserted the multiplication symbols.

\(6\cdot b\cdot\sqrt{16} = 6\cdot b\cdot 4\)

Does that make sense?

Answer 18

Yes

Answer 19

Excellent. Now, write the whole expression with that substitution. ONLY that substitution.

Answer 20

\[\sqrt{2}(6b4-2b)\]

Answer 21

Got it. Can we now simplify 6*b*4? Maybe 6*4*b = 24b?

Answer 22

\[\sqrt{2}(24b-2b)\]

Answer 23

Can we now simplify what is inside the parentheses?

Answer 24

yes

Answer 25

What say you?

Answer 26

do i subtract 24b and 2b?

Answer 27

Is that what the expression indicates?

Answer 28

Can you subtract them? Are they the same sort of thing?

Answer 29

i think so their like terms

Answer 30

Very good. Subtract away!

Answer 31

\[\sqrt{2}(22b)\]

Answer 32

Are we done or is there more to do.

Answer 33

We multiply

Answer 34

We are simplifying. That is all we are doing. Do you see any multiplication in there that will SIMPLIFY the expression?

Answer 35

yes

Answer 36

Really? I don't. What are you planning?

Answer 37

no there is none

Answer 38

the question what is the product so i thought you had to multiply

Answer 39

It is multiplication, but the task is to simplify. When operations fail to simplify, quit.

\(\sqrt{2}(22b) = 22\sqrt{2}\cdot b = 22b\sqrt{2}\)

They are all equivalent and they are all about the same complexity. I think we're done.

Answer 40

oh ok

Answer 41

Thank you so much for your help!

Answer 42

:)

Answer 43

No worries. It's what we do here.

Thank you for hanging in there and getting all the way through it!

Answer 44

Your welcome . I understand so much better now.