Home > Algebra > Multiplication and Division of Radicals

How do you rationalize the denominator and simplify #14/ (sqrt7-sqrt5)#?

Answer 1

Hazel Anglin

# 7sqrt7 + 7sqrt5#

You can multiply #sqrt7 - sqrt5# with #sqrt7 + sqrt5# which would result in 2. So you would have;

# (14 × (sqrt7 + sqrt5)) / 2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jameson Allen

To rationalize the denominator and simplify the expression 14/ (sqrt7-sqrt5), we can multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt7+sqrt5. This will eliminate the square root in the denominator.

By applying the conjugate, we get: 14(sqrt7+sqrt5) / ((sqrt7-sqrt5)(sqrt7+sqrt5))

Simplifying further: 14(sqrt7+sqrt5) / (7 - 5)

The denominator simplifies to 2, so the final simplified expression is: 7(sqrt7+sqrt5)

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.