Divide square rootsRationalize a one-term denominatorRationalize a two-term denominator

Divide Square Roots

We know that we leveling fractions by removing factors common to the numerator and the denominator. Once we have a fraction with a square root in the numerator, we an initial simplify the square root. Then we can look for common factors.

You are watching: How to divide fractions with square roots

*
.


*
. This is lot easier.

Even despite we have calculators easily accessible nearly everywhere, a portion with a radical in the denominator still have to be rationalized. It is not considered simplified if the denominator includes a square root.

Similarly, a square root is not considered simplified if the radicand includes a fraction.


Simplified Square Roots

A square root is thought about simplified if there are

no perfect-square components in the radicandno fractions in the radicandno square roots in the denominator that a fraction

To rationalize a denominator, we use the building that

*
.
*
Remove typical factors.
*

Simplify:

*
Simplify the denominator
*
Simplify.
*

Simplify:

*
Simplify the denominator.
*
Simplify.
*

Simplify:

*
Multiply the conjugates in the denominator.
*
Simplify the denominator.
*
We leave the numerator in factored form to do it less complicated to look for typical factors after we have actually simplified the denominator.

Simplify:

*
Multiply the conjugates in the denominator.
*
Simplify the denominator.
*

Simplify:

*
Multiply the conjugates in the denominator.
*

Simplify:

*
Multiply the conjugates in the denominator.
*
We execute not square the numerator. In factored form, we deserve to see there are no common factors to remove from the numerator and also denominator.

See more: How To Say Never In French = Ne (Verb) Jamais, Jamais: Never, Ever, Forever


Simplify:

*

Elementary Algebra by OSCRiceUniversity is license is granted under a an imaginative Commons Attribution 4.0 worldwide License, other than where otherwise noted.