Rationalize the denominator and simplify: sqrt a/8- sqrt a
To rationalize the denominator and simplify the expression sqrt(a)/8 - sqrt(a), we need to get rid of the square root in the denominator.
First, let's rewrite the expression as:
sqrt(a) / 8 - sqrt(a) = sqrt(a) / 8 - 8 * sqrt(a) / 8
Next, to combine the terms, we need a common denominator. In this case, the common denominator is 8. Therefore, we can rewrite the expression as:
(sqrt(a) - 8 * sqrt(a)) / 8
Now, combine the terms in the numerator:
(sqrt(a) - 8 * sqrt(a)) = (1 - 8)sqrt(a) = -7sqrt(a)
So, putting it all together, the simplified and rationalized expression is:
-7sqrt(a) / 8