Question

How would 4/(5-sq rt of 13) be equal to 5+ sq rt of 13/3?

Answer 1

Rationalize the denominator

Answer 2

so multiply both sides by 5- radical 13?

Answer 3

\[\frac{ 4 }{ 5 \space - \sqrt{13} } \space . \frac{ 5 \space + \sqrt{13} }{ 5 \space + \sqrt{13} } \space = \frac{ 4 ( 5+ \sqrt{13 \space )} }{ 5^{2 \space - (\sqrt{13)^{2}}} }\]

Answer 4

\[= \frac{ 45 + \sqrt{13}}{ 25 - 13 } \space = \frac{ 14 (5+\sqrt{13} }{ 3 } \space = \frac{ 5+\sqrt{13} }{ 3 }\]

Answer 5

If I multiplied by 5- sq rt of 13, would I get the same answer?

Answer 6

5+sqrt(13) is the conjugate of 5-sqrt(!3).

Answer 7

You have to multiply 5+sqrt(13) which is the conjugate of 5-sqrt(13).

Answer 8

So anytime the denominator has a form of radical like this, always multiply by conjugates, right?

Answer 9

Right

Answer 10

Thank you

Answer 11

In that way, we can get rid of radicals.