Question

Rationalize the denominator and simplify.

Answer 1

Hi, welcome to OpenStudy.

Answer 2

thanks

Answer 3

To rationalize the denominator, you must multiply the numerator and denominator by the conjugate of the denominator.

What is the conjugate of \(\sqrt{a}-2\sqrt{y}\)?

Answer 4

you would just switch the subtraction to addition right?

Answer 5

how did you make that square root symbol

Answer 6

It's called latex.

`\(\sqrt{a}\)`

That's the code to do it. You can also use the equation button to do it easier :)

Answer 7

ok cool so wouldnt it be

Answer 8

\[\sqrt{a}+2\sqrt{y}\]

Answer 9

Correct!

Answer 10

So now, lets do the multiplication.

\(\Large\frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}-2\sqrt{y}}\times \frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}+2\sqrt{y}}=?\)

Answer 11

Hint:

\(\sf\Large (x+y)(x+y)=x^2+2xy+y^2\)

\(\sf\Large (x+y)(x-y)=x^2-y^2\)

Answer 12

you lost me

Answer 13

Ok, lets multiply the numerators first.

\(\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?\)

Answer 14

Use the formula I gave you above.

Answer 15

\[\sqrt{a^2}+4\sqrt{y^2}\]

Answer 16

?

Answer 17

No...

Answer 18

\(\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?\)

Use the formula:
\(\sf\Large (x+y)\times (x+y)= x^2+2xy+y^2\)

remember: x, y, a, and b are all variables.

Answer 19

im lost

Answer 20

@Lyralei
can you help me

Answer 21

Where are you lost at?