Question

Math Review Day 3!

6e. Rationalize the expression and simplify.

Answer 1

Let me re-type the question

6e. Rationalize the expression and simplify

\(\huge\frac{\sqrt{4+h}-2}{h}\)

Answer 2

Is this root just for 4? Or h also?

Answer 3

the root is \(\sqrt{4+h}\) @joyraheb

Answer 4

i guess multiply the numerator and the denominator by the `conjugate` of the numerator

Answer 5

I do believe that the first step would be to multiply the whole expression by the conjugate of the numerator. So I assume that it would look a little like this:

\(\huge\frac{\sqrt{4+h}-2}{h}\times\huge\frac{\sqrt{4+h}+2}{\sqrt{4+h}+2}\)

Answer 6

LOL you read my mind XD There is a lot of multiplying of conjugates in Algebra. A common trend that I recall

Answer 7

If you multiply these, you should get

\(\huge\frac{(4+h)-4}{h(\sqrt{4+h}+2}\)

right?

Answer 8

yes right!

Answer 9

yes! oops wait i think a parentheses is missing in in the denominator

\(\huge\frac{(4+h)-4}{h(\sqrt{4+h})+2}\)

Answer 10

anyhow, from here I'm a little stuck. I know the in the numerator, 4 and -4 cancel out, so you're left with h...but what happens in the denominator?

Answer 11

yes right
\(\huge\rm \frac{\color{reD}{4}+h\color{reD}{-4}}{h(\sqrt{4+h}+2)}\)\[\rm \frac{ h }{ h(\sqrt{4+h}+2)}\]
can you cancel out anything ?

Answer 12

oh wait! i see. So i mentioned canceling out in the numerator, but it seems like something in the numerator and denominator can be cancelled out
\(\huge\rm \frac{\color{reD}{4}+\color{green}h\color{reD}{-4}}{\color{green}h(\sqrt{4+h}+2)}\)

The things in green become 1, so wouldn't you have this:

\(\huge\frac{1}{\sqrt{4+h}+2}\)

Answer 13

parentheses should be aftr 2
cuz it's one expression (sqrt{4+h}+2)

Answer 14

that's right!

Answer 15

oh true, whoops XD and ty ;-;

Answer 16

np don't cry:(

Answer 17

yeah i put the parentheses in the wrong place earlier. my bad

hehe I'm fine. From there, am I done?

Answer 18

is that the final answer?

Answer 19

btw do you have the answer ?
just want to know cuz most of times we r not allowed to leave the square root at the denominator

Answer 20

yes i think so we can't do anything else with that exprssion

Answer 21

hmmm lemme check online. The textbook doesn't have the answers in it, but the textbook's website has them. Brb

Answer 22

oh cool

Answer 23

Yep that's it. Thank you thank you! XD

Answer 24

my pleasure