How do you rationalize the denominator and simplify $4/(6-sqrt5)$ ?

Question

1151 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-27T12:08:26

$= (24 + 4 sqrt5)/ (31)$

$4 / ( 6 -sqrt5)$

To rationalize the denominator, we multiply the expression , by the conjugate of the denominator.

Conjugate , of $6 -sqrt5 = color(blue)( 6 + sqrt5$

$4 / ( 6 -sqrt5) = (4 * (color(blue)( 6 + sqrt5))) / (( 6 -sqrt5) * color(blue)( 6 + sqrt5)$

Applying below mentioned property to simplify denominator:
$color(blue)((a-b)(a+b) = a^2 - b^2$

$= (4 * (color(blue)( 6)) + 4 * (sqrt5))/ (( 6 ) ^2 -(sqrt5)^2)$

$= (24 + 4 sqrt5)/ ((36 - 5)$

$= (24 + 4 sqrt5)/ (31)$

How do you rationalize the denominator and simplify 4/(6-sqrt5)4/(6-sqrt5)?