divide √95 by 3√5. provide an exact answer
To divide √95 by 3√5, we can rationalize the denominator.
First, let's simplify the expression:
√95 ÷ 3√5 = (√(19 × 5)) ÷ (3√5) = (√19 √5) ÷ (3√5) = (√19 / √5) ÷ (3√5).
Now, let's rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is √5:
(√19 / √5) ÷ (3√5) × (√5 / √5) = (√19 √5) / (3√5 × √5) = (√19 √5) / (3(√5)^2) = (√19 √5) / (3 × 5) = (√19 √5) / 15.
Therefore, the exact answer is (√19 √5) / 15.
To divide √95 by 3√5 and provide an exact answer, we can simplify the expression by rationalizing the denominator.
First, let's write the expression as a fraction: √95 / 3√5.
To rationalize the denominator, we need to eliminate the square root in the denominator.
To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is 3√5.
(√95 / 3√5) * (3√5 / 3√5) = (3√(95 * 5)) / (9 * 5)
Simplifying further:
= √(3^2 * 5 * 19) / (9 * 5)
= (3√(285)) / 45
So the exact answer for √95 / 3√5 is (3√(285)) / 45.
To divide √95 by 3√5, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of 3√5, which is (3√5)(√5). Simplifying this, we get:
(√95)/(3√5) * (√5)/(√5) = (√(95*5))/(3*5)
= (√475)/(15)
= (√19*5)/(15)
= (√19/√5)*(√5/√5)
= (√19)/(√5)*(√5)/(√5)
= (√19*√5)/(√5*√5)
= √(19*5)/(√(5*5))
= √(95)/5
Therefore, √95 divided by 3√5 is equal to √95/5.