Divide √95 / 3√5 Provide an exact answer.
To divide √95 by 3√5, we can simplify the expression by rationalizing the denominator.
√95 can be written as √(19 * 5) which is equal to √19 * √5.
Let's substitute these values into the expression:
(√19 * √5) / (3√5)
Now, we can cancel out the √5 terms:
(√19 * √5) / (3 * 1)
Simplifying further:
(√19 * √5) / 3
Since the terms inside the square roots cannot be simplified further, the exact answer is (√19 * √5) / 3.
To divide the expression (√95) / (3√5) and obtain an exact answer, we need to rationalize the denominator. Rationalizing the denominator means eliminating any radicals in the denominator.
Step 1: Recall the property of radicals that states √a / √b = √(a/b). Using this property, we can rewrite the denominator as √5 * √5 = 5.
Step 2: Simplify the expression to (√95) / (3√5) * (√5/√5).
Step 3: Combine the radicals in the numerator: √(95*5) / 3√5.
Step 4: Evaluate the expression in the numerator: √(475) / 3√5.
Step 5: Since the denominator is in the form of a radical, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of 3√5 is -3√5.
Step 6: Multiply the numerator and denominator by -3√5: (√(475) * -3√5) / (3√5 * -3√5).
Step 7: Simplify the expression: (-3√(475*5)) / (-3 * √(5*5)).
Step 8: Evaluate the expression: (-3√2375) / (-3√25).
Step 9: Simplify further: (√2375) / √25.
Step 10: Simplify √25 to 5: (√2375) / 5.
Therefore, the exact answer is (√2375) / 5.
To divide √95 by 3√5, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
The conjugate of 3√5 is (3√5)(√5)/(√5)(√5) = 3√5/5.
So, the expression becomes (√95 / 3√5) * (3√5 / 3√5) = (3√95 * 3√5) / (3√5 * 3√5) = 9√(95*5) / 9 * 5 = 9√(475) / 45.
Thus, the exact answer is √(475) / 5.