How do you simplify $(12sqrt9)/sqrt18$ ?

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Answer 1 · 2016-04-17T17:17:58

$= 6sqrt2$

$(12sqrt9)/ sqrt18$

$sqrt 9 = sqrt ( 3 *3 ) = color(green)(3$

$sqrt18 = sqrt ( 2 * 3 * 3 ) = sqrt ( 2 * 3 ^2) = color(green)( 3 sqrt2$

Our expression now becomes
$(12 * color(green)((3)))/ color(green)( 3 sqrt2$

$= (12 * color(green)(cancel(3)))/ color(green)( cancel3 * sqrt2$

$= 12 / sqrt2$

Rationalising the denominator:
$= (12 * sqrt2) / (sqrt2 * sqrt2)$

$= (12 * sqrt2) / 2$

$= (cancel12 * sqrt2) / cancel 2$

$= 6sqrt2$

How do you simplify (12sqrt9)/sqrt18(12sqrt9)/sqrt18?