Question

Rationalize the denominator of

Answer 1

https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l6%2050.jpg

Answer 2

@calculusxy

Answer 3

@agent0smith

Answer 4

@TheSmartOne

Answer 5

@Anaise

Answer 6

To rationalize the denominator, multiply the top and bottom by whatever is in the square root of denominator because

\(\sqrt{a} \times \sqrt{a} = a\)

so for example

\(\Large\frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} =\boxed{\bf{\frac{\sqrt{2}}{2} }}\)

Answer 7

rationalizing the denominator basically means removing the square root from the denominator

Answer 8

so the 6?

Answer 9

-5

-1
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l8%2013.jpg
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l8%2012.jpg
these are my choices

Answer 10

what is under the square root in the question, not the answer choices

Answer 11

6

Answer 12

6 is in the answer choices, what is it in the question? https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l6%2050.jpg

Answer 13

its \[\sqrt{6}\]

Answer 14

@TheSmartOne

Answer 15

http://prntscr.com/bknf6b

Answer 16

I said the question, not the answer choices.

Answer 17

no i know the denomentor has square root 6

Answer 18

@TheSmartOne

Answer 19

what is in the red box? http://prntscr.com/bknf6b

Answer 20

oh my gosh i just realized that i was looking at the wrong problem... that is why i was saying 6.... sorry

Answer 21

I was wondering what was wrong, haha

Answer 22

5zr is in the red box

Answer 23

i am so sorry

Answer 24

so, we have to multiply top and bottom by it

\(\Large\bf \frac{\sqrt{20z^2r}}{\sqrt{5zr}} \times \frac{\sqrt{5zr}}{\sqrt{5zr}} =\)

Answer 25

so would i multiply 100z^3r^2 for the numerator or no?

Answer 26

that's correct, and it's under a sqrt

Answer 27

right

Answer 28

and what would the denominator be?

Answer 29

ok so what do i have to do?

Answer 30

25z^2 r^2

Answer 31

under a sqrt

Answer 32

remember

\(\sqrt{a} \times \sqrt{a} = a\)

if we use that, then the denominator simply loses the sqrt sign and becomes 5zr

do you understand?

Answer 33

oh got it

Answer 34

now let's simplify

\(\sqrt{100z^3r^2}\)

Answer 35

10 is sqrt of 100 r is squrt of r

Answer 36

@TheSmartOne

Answer 37

and here is another hint:

\(\sqrt{z^3} = \sqrt{z^2 \times z} = \sqrt{z^2}\sqrt{z} = \)

Answer 38

so \[2\sqrt{z}\]

Answer 39

@TheSmartOne

Answer 40

not sure where that 2 came from

remember this rule:
\(\sqrt{a^2} = a\)

Answer 41

\[\sqrt{z^2}\]

Answer 42

@TheSmartOne

Answer 43

mhmmm, no

\(\sqrt{z^3} = \sqrt{z^2 \times z} = \sqrt{z^2}\sqrt{z} = \)

so simplify \(\sqrt{z^2}\)

Answer 44

or just \[\sqrt{z}\]

Answer 45

z

Answer 46

@TheSmartOne

Answer 47

yes, so it is \(z\sqrt{z}\)

Answer 48

now we have

\(\Large\frac{10zr\sqrt{z}}{5zr}\)

Answer 49

ok so 10/5 is 2 zr ar cancelled out so that leaves
\[2\sqrt{z}\]

Answer 50

@TheSmartOne

Answer 51

yes :)

Answer 52

I have a couple more like this could you help me with them?

Answer 53

?

Answer 54

Rationalize the denominator of https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l8%2011.jpg
@TheSmartOne