solve: √95 / (3√5)
To solve √95 / (3√5), we can simplify the expression as follows:
√95 / (3√5) = (√(19*5)) / (3√5)
Using the property √(ab) = √a * √b:
= (√19 * √5) / (3√5)
The square root of 5 in the numerator cancels out with the square root of 5 in the denominator:
= √19 / 3
Therefore, the simplified form of √95 / (3√5) is √19 / 3.
To simplify the expression √95 / (3√5), we can multiply the numerator and denominator by the conjugate of the denominator. The conjugate is obtained by changing the sign of the second term.
The conjugate of 3√5 is -3√5.
Multiplying the numerator and denominator by -3√5, we have:
[ √95 / (3√5) ] * [-3√5 / -3√5]
This simplifies to:
(-3√(95√) / (3√5)(-3√5))
Simplifying further:
√(95√) / (-3√5)(-3√5)
The denominator simplifies to:
(-3√5)(-3√5) = (-3*-3)(√5*√5) = 9(5) = 45
So, the simplified expression is:
√(95√) / 45
To solve this expression, we need to simplify it step by step.
First, let's simplify the radicals separately.
The square root of 95 can be written as √(5 * 19). Since we can't simplify the square root of 19 any further, we keep it outside the radical: √(5 * 19) = √5 * √19.
Next, let's simplify the cube root of 5. Since there are no perfect cube factors of 5, we keep it as 3√5.
Now, let's substitute these simplified expressions back into the original expression:
√95 / (3√5) = (√5 * √19) / (3√5).
Now, we can cancel out the common factor of √5 in the numerator and the denominator.
(√5 * √19) / (3√5) = (√19) / 3.
So the simplified form of the expression √95 / (3√5) is (√19) / 3.