how to simplify 2√4-√9?

- Anguyennn

how to simplify 2√4-√9?

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- jim_thompson5910

What is the square root of 4 equal to?

- Anguyennn

2

- jim_thompson5910

correct
What is the square root of 9 equal to?

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## More answers

- Anguyennn

3

- Anguyennn

and you multiply 2x2 and minus 3? correct?

- jim_thompson5910

so you really have `2*2-3`
evaluate that to get ??

- jim_thompson5910

correct

- Anguyennn

oh ok!! thank you but what about when its √2?

- jim_thompson5910

taking the square root of 2 doesn't give a whole number like the square root of 4 does

- Anguyennn

like 3√2-5√2-2√2

- jim_thompson5910

I don't see a square root of 2 in your problem though

- jim_thompson5910

Oh I see now

- jim_thompson5910

replace every copy of "square root of 2" with x
so you'll have 3x-5x-2x
simplify that to get ???

- Anguyennn

-4x

- Anguyennn

but how come you replaced it with an x?

- jim_thompson5910

well you don't need to, but you can think of it like that
basically you're combining like terms. In this case, all 3 terms are like terms because they have a root 2 in them

- Anguyennn

yes

- jim_thompson5910

3x-5x-2x = -4x
so you now replace the x with square root of 2
so the final answer is \(\Large -4\sqrt{2}\)

- Anguyennn

i am still confused because for other questions it would have different numbers and i don't know how to do them

- jim_thompson5910

like what for example?

- Anguyennn

√18+√50-√8

- jim_thompson5910

have you tried to simplify each root?

- Anguyennn

dividing them all by 2?

- jim_thompson5910

think of all of the factors of 18
which factors are perfect squares?

- Anguyennn

I am not sure

- Anguyennn

sorry

- jim_thompson5910

factors of 18
1,2,3,6,9,18

- Anguyennn

ok

- jim_thompson5910

which factor is a perfect square?

- Anguyennn

9

- jim_thompson5910

so we can say this
\[\Large \sqrt{18} = \sqrt{9*2}\]
\[\Large \sqrt{18} = \sqrt{9}*\sqrt{2}\]
\[\Large \sqrt{18} = 3*\sqrt{2}\]

- jim_thompson5910

I factored 18 into 9*2
then I used the rule \[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

- Anguyennn

yes

- jim_thompson5910

now let's do 50
what are the factors of 50?

- Anguyennn

1, 2, 5, 10, 25

- Anguyennn

and it would be 25 that is the perfect square

- jim_thompson5910

yes so 50 = 25*2

- jim_thompson5910

what would \(\Large \sqrt{50}\) simplify to?

- Anguyennn

√25x2

- jim_thompson5910

then break it up using the rule I posted

- Anguyennn

√50= √25x2
=√25x √2
5√2

- jim_thompson5910

good

- jim_thompson5910

now onto 8
the factors of 8 are ???

- Anguyennn

1,2,4,8

- jim_thompson5910

which is a perfect square?

- Anguyennn

√4

- jim_thompson5910

so we can say 8 = 4*2

- jim_thompson5910

then use that rule

- Anguyennn

√8= √4x2
=√4x√2
2√2

- jim_thompson5910

so,
\[\Large \sqrt{18}+\sqrt{50}-\sqrt{8}\]
is the same as
\[\Large 3\sqrt{2}+5\sqrt{2}-2\sqrt{2}\]

- jim_thompson5910

we can replace all the square root of 2 terms with x
\[\Large 3\color{red}{\sqrt{2}}+5\color{red}{\sqrt{2}}-2\color{red}{\sqrt{2}}\]
\[\Large 3\color{red}{x}+5\color{red}{x}-2\color{red}{x}\]

- Anguyennn

correct

- Anguyennn

is that the answer?

- jim_thompson5910

not yet

- Anguyennn

would you do 3+5-2 now?

- Anguyennn

and get 6√2?

- jim_thompson5910

very good, that's your final answer

- Anguyennn

oh ok thank you so much!

- jim_thompson5910

you're welcome

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