x^1/2 * y^1/6 *z^1/5. We are to use rational exponents to write an expression.
The sqrt of x - the sqrt of y, over the sqrt of x + the sqrt of y. I need to simplify and use radicals as needed. I obviously do but what...?? Please assist.
Thank you.
I'm not quite sure I understand the second question, but I'll take a guess. You want to simplify
{sqrt(x) - sqrt(y)} / {sqrt(x) + sqrt(y)}.
Multiply the top and bottom of this expression by {sqrt(x) - sqrt(y)}. The numerator will then be {x - 2.sqrt(xy) + y}, and the denominator will be (x - y). You've now only got square roots in the numerator. Is that what you need?
To simplify the expression involving square roots, we can follow these steps:
Step 1: Identify the common denominator by multiplying the denominators of the two fractions. Here, we have the square root of x and the square root of y, so the common denominator is (sqrt(x))^2 * (sqrt(y))^2.
Step 2: Simplify the numerator by subtracting the square roots. This gives us (sqrt(x) - sqrt(y)).
Step 3: Simplify the denominator by adding the square roots. This gives us (sqrt(x) + sqrt(y)).
Step 4: Combine the simplified numerator and denominator to get the final expression:
(sqrt(x) - sqrt(y))/(sqrt(x) + sqrt(y))
This is the simplified expression using radicals as needed.