Divide √95/3√5 . Provide an exact answer.
To divide √95 by 3√5, we need to rationalize the denominator:
√95/3√5 * (√5√5)/ √5√5
This gives us:
(√475)/(3√25)
Now, simplify by factoring out perfect squares from the numerator and denominator:
(√(25*19))/(3*√25)
√(25*19) is equal to √25 * √19, which simplifies to 5√19.
So the final answer is:
(5√19)/(3*5)
Cancel out the factor of 5 from the numerator and denominator:
(√19)/3
answer
The exact answer is (√19)/3.
To divide √95 by 3√5, we can simplify the expression by first rationalizing the denominator. We can multiply the denominator and numerator of the expression by the conjugate of the denominator, which in this case is 3√5.
Let's expand the expression:
√95 / 3√5 = (√95 * 3√5) / (3√5 * 3√5)
To simplify further, we can multiply the square roots:
= (3√(95 * 5)) / (3 * √(5 * 5))
Simplifying gives us:
= (3√(475)) / (3 * 5)
Now, we can cancel out the 3's:
= √(475) / 5
Therefore, the exact answer to √95 / 3√5 is √(475) / 5.