Question

If h ≠ 0 , rationalize the numerator of (√x+h - √x) /h.

Answer 1

help me please! I need to submit the answer by tomorrow..

Answer 2

so do you know what mean rationalizing the numerator ?

Answer 3

actually i don't know,, i don't understand about this topic.. can you show how to solve it?

Answer 4

so in case of the first term in numerator there x and h are inside radical too ,yes ?

Answer 5

okay..

Answer 6

so than there you need getting the numerator without radical

what you think how will can getting this ?

Answer 7

so for your help in the first step try seeing this numerator in the form of (a -b)

so because i think that you know sure the formula (a-b)(a+b)=a^2 -b^2

Answer 8

i have no idea.. let me try! do we need to conjugate the numerator??

Answer 9

yes exactly and hence will eliminate the radical from there

ok ?

Answer 10

ok

Answer 11

try it here now for i can check it if is correct ,ok ?

Answer 12

ok

Answer 13

did the answer is √h / h...

Answer 14

is my answer correct?

Answer 15

(√x+h - √x) /h.

how you have got it ?

Answer 16

first i conjugate the numerators by multiply the numerators with h..

Answer 17

no

i have wrote above what you need using

formula

a^2 -b^2 =(a-b)(a+b)

so there now in numerator consider that is (a-b)

so for you can getting a^2 -b^2 ,you need multiplie it by (a+b)

yes ?

so this using you will get a^2 -b^2 and hence do you know that a squaroot squared will eliminate the squaroot

yes ?

can you using this easy now here ?

Answer 18

can you show the step to solve it first,, then you explain it to me.. Can you??

Answer 19

ok

(√x+h - √x) /h.

(sqrt(x+h) -sqrt(x) so here for you can eliminate the radicale you need multiplie by

(sqrt(x+h) + sqrt(x) ,yes --- but for you can doing this you need multiplie the denominator too by (sqrt(x+h) + sqrt(x)

so because you know that (sqrt(x+h) + sqrt(x)) /(sqrt(x+h) +sqrt(x)) = 1 and hence you will have there the originale fraction little extended but not modified

hope you understand me

(sqrt(x+h) -sqrt(x)) (sqrt(x+h) -sqrt(x))*(sqrt(x+h) +sqrt(x))
----------------- = ----------------------------------- =
h h*(sqrt(x+h) +sqrt(x))


(sqrt(x+h))^2 - (sqrt(x))^2 x+h -x
= ------------------------- = ------------------- =
h*(sqrt(x+h) +sqrt(x)) h*(sqrt(x+h) +sqrt(x))


h
= -------------------
h*(sqrt(x+h) +sqrt(x))

hope so much that you will can understanding all right easy

Answer 20

ok ?

Answer 21

ok.. can i ask you another question??

Answer 22

yes try it on the open question column please

Answer 23

so, is this the final answer?? h
= -------------------
h*(sqrt(x+h) +sqrt(x))

Answer 24

A ball is dropped from a height of 1 m onto the floor. After its first bounce, it rises to a height of 49 cm.
a) Call the height after the nth bounce hn. Find a formula for hn and say what happens to hn as n gets larger.
b) Under these circumstances the time between the first and second bounces is 0.6321 seconds. Call this t1. The next time, t2, is 0.7 times the previous one. Find the formula for tn.
c) If S1=t1+t2, what does S2 represent? Calculate S20, and S50. How long after the first bounce does the ball stop bouncing altogether, to the nearest tenth of a second?

Answer 25

that is my second question