simplify (4\sqrt(6))/(\sqrt(30)) by rationalizing the denominator. Show all the work, please
To simplify (4√6)/(√30) by rationalizing the denominator, let's first rewrite the expression with the radicals fully expanded:
(4 * √6) / (√(2 * 3 * 5))
Now we can simplify further by breaking down the radical in the denominator:
(4 * √6) / (√2 * √3 * √5)
= (4 * √6) / (√2 * 3√5)
= (4√6) / (3√10)
Now, to rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator:
= (4√6 * 3√10) / (3√10 * 3√10)
= 12√60 / 9 * 10
= 12√60 / 90
= (12 * 2√15) / 90
= 24 / 45
= 8 / 15
Therefore, the simplified form of (4√6) / (√30) after rationalizing the denominator is 8/15.