Question

Need help with Radical Expressions and Equations

Answer 1

simplify

Answer 2

multiply by the conjugate

Answer 3

Do you know how?

Answer 4

It's kind of like multiplying by the opposite sign..
\[\frac{ 2 }{ \sqrt7-\sqrt5 }*\frac{ \sqrt7+\sqrt5 }{ \sqrt7+\sqrt5 }\]

Answer 5

Oh okay, I knew that but I wasnt sure if instead of division I would multiply.
I dont understand why is has the division sign in front of 7 and 5?

Answer 6

When doing conjugates you multiply top and bottom. So multiply them out and tell me what you get.

Answer 7

Not exactly..

Answer 8

Bahhhhhh so confused guifaljkgf

Answer 9

\[\frac{ 2 }{ \sqrt7-\sqrt5 }*\frac{ \sqrt7+\sqrt5 }{ \sqrt7+\sqrt5 }=\frac{ 2(\sqrt7+\sqrt5) }{ (\sqrt7-\sqrt5)(\sqrt7+\sqrt5) }\]

Answer 10

Can multiply it now?

Answer 11

ahemm, keep in mind that
\(a^2-b^2) = (a-b)(a+b)\)
so
\( (\sqrt{a}+\sqrt{b}) \times (\sqrt{a}-\sqrt{b}) \implies (\sqrt{a})^2 + (\sqrt{b})^2 = a+b\)

Answer 12

thus, the use of the conjugate

Answer 13

well, that went a bit bonk, lemme rewrite that :/

Answer 14

$$
(\sqrt{a}+\sqrt{b}) \times (\sqrt{a}-\sqrt{b}) \implies (\sqrt{a})^2 - (\sqrt{b})^2 = a-b
$$

Answer 15

Haha, oh jdoe :P