Divide √95 / 3√5 . Provide an exact answer. (1 point)

Answer 1

To divide √95 by 3√5, we multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of 3√5 is 3√5, so the expression becomes:

(√95 / 3√5) * (3√5 / 3√5)

This simplifies to:

(3√95 * √5) / (3√5 * 3√5)

Taking the product of the numerators gives:

3√(95 * 5) / (3√(5 * 5 * 5))

This simplifies further to:

3√475 / (3√125)

Now, we can simplify the radicals:

3 * (√(475) / √(125))

√475 = √(25 * 19) = 5√19

√125 = √(25 * 5) = 5√5

Plugging these values in, we get:

3 * (5√19 / 5√5)

The 5's cancel out, leaving us with:

3 * √19 / √5

Therefore, the exact answer is 3√19 / √5.