Divide √95/3√5 Provide an exact answer.
To divide √95 by 3√5, we multiply the numerator and denominator by the conjugate of the denominator to rationalize the denominator.
Conjugate of 3√5 is 3√5.
√95/3√5 * 3√5/3√5
= (3√95 * 3√5) / (3√5 * 3√5)
= 9√(95 * 5) / (3 * 5)
= 9√475 / 15
= (9/15) * √475
= (3/5) * √475
Therefore, the exact answer is (3/5) * √475.
To divide √95 by 3√5, we need to rationalize the denominator.
First, we multiply both the numerator and denominator by the conjugate of the denominator, which is √5:
√95/3√5 * (√5/√5) = (√95 * √5)/(3 * √5 * √5)
Simplifying further:
= √(95 * 5)/(3 * 5)
= √475/15
Therefore, the exact answer is √475/15.
To divide the expression √95 by 3√5, we need to rationalize the denominator.
Step 1: Simplify the expression.
√95 can be broken down as √(19 * 5) which equals √19 * √5.
So, √95 becomes √19 * √5.
Step 2: Rationalize the denominator.
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of 3√5 is 3√5 itself (since there is no sum or difference of radicals in the denominator).
(√19 * √5) / (3√5) * (3√5) / (3√5)
Applying the multiplication, we get:
(√19 * √5 * 3√5) / (3 * √5 * 3√5)
Step 3: Simplify the expression.
Multiplying the terms in the numerator and denominator, we have:
(√19 * √5 * 3 * √5) / (3 * √5 * 3 * √5)
Now, cancel out the √5 terms in the numerator and denominator:
(√19 * 3) / (3 * 3)
Simplifying further:
√19 / 3
Therefore, the exact answer to the expression (√95) / (3√5) is √19 / 3.