Question

how to simplify 2√4-√9?

Answer 1

What is the square root of 4 equal to?

Answer 2

2

Answer 3

correct

What is the square root of 9 equal to?

Answer 4

3

Answer 5

and you multiply 2x2 and minus 3? correct?

Answer 6

so you really have `2*2-3`

evaluate that to get ??

Answer 7

correct

Answer 8

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

Answer 9

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

Answer 10

like 3√2-5√2-2√2

Answer 11

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

Answer 12

Oh I see now

Answer 13

replace every copy of "square root of 2" with x

so you'll have 3x-5x-2x

simplify that to get ???

Answer 14

-4x

Answer 15

but how come you replaced it with an x?

Answer 16

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

Answer 17

yes

Answer 18

3x-5x-2x = -4x

so you now replace the x with square root of 2

so the final answer is \(\Large -4\sqrt{2}\)

Answer 19

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

Answer 20

like what for example?

Answer 21

√18+√50-√8

Answer 22

have you tried to simplify each root?

Answer 23

dividing them all by 2?

Answer 24

think of all of the factors of 18

which factors are perfect squares?

Answer 25

I am not sure

Answer 26

sorry

Answer 27

factors of 18

1,2,3,6,9,18

Answer 28

ok

Answer 29

which factor is a perfect square?

Answer 30

9

Answer 31

so we can say this

\[\Large \sqrt{18} = \sqrt{9*2}\]

\[\Large \sqrt{18} = \sqrt{9}*\sqrt{2}\]

\[\Large \sqrt{18} = 3*\sqrt{2}\]

Answer 32

I factored 18 into 9*2

then I used the rule \[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

Answer 33

yes

Answer 34

now let's do 50

what are the factors of 50?

Answer 35

1, 2, 5, 10, 25

Answer 36

and it would be 25 that is the perfect square

Answer 37

yes so 50 = 25*2

Answer 38

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

Answer 39

√25x2

Answer 40

then break it up using the rule I posted

Answer 41

√50= √25x2
=√25x √2
5√2

Answer 42

good

Answer 43

now onto 8

the factors of 8 are ???

Answer 44

1,2,4,8

Answer 45

which is a perfect square?

Answer 46

√4

Answer 47

so we can say 8 = 4*2

Answer 48

then use that rule

Answer 49

√8= √4x2
=√4x√2
2√2

Answer 50

so,

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

Answer 51

we can replace all the square root of 2 terms with x

\[\Large 3\color{red}{\sqrt{2}}+5\color{red}{\sqrt{2}}-2\color{red}{\sqrt{2}}\]
\[\Large 3\color{red}{x}+5\color{red}{x}-2\color{red}{x}\]

Answer 52

correct

Answer 53

is that the answer?

Answer 54

not yet

Answer 55

would you do 3+5-2 now?

Answer 56

and get 6√2?

Answer 57

very good, that's your final answer

Answer 58

oh ok thank you so much!

Answer 59

you're welcome