Final answer:
To simplify the expression √(5/8), you can simplify the numerator and denominator separately. The square root of 8 can be simplified to 2√2. Rationalizing the denominator, the final simplified form is √10 / 4.
Step-by-step explanation:
To simplify the expression √(5/8), we can first simplify the numerator and denominator of the fraction separately. The square root of 5 is not a perfect square, so we cannot simplify it further. The square root of 8, however, can be simplified. We can write 8 as 4 * 2, and since 4 is a perfect square, we can take its square root. So, we have √(5/8) = √5 / √8.
Next, we can simplify the square root of 8. √8 can be written as √4 * √2, and since √4 is 2, we have √8 = 2√2. Substituting this back into our expression, we get √(5/8) = √5 / 2√2.
Finally, we can simplify the expression further by rationalizing the denominator. We can multiply the numerator and denominator by √2 to get rid of the radical in the denominator. This gives us the final simplified form: √(5/8) = (√5 * √2) / (2√2 * √2) = (√10) / (2 * 2) = √10 / 4.