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

Divide Square Roots

We know that we leveling fractions by removed factors common to the numerator and also the denominator. Once we have a portion with a square root in the numerator, we very first simplify the square root. Climate we deserve to look for usual factors.

You are watching: How to divide fractions with square roots

*
.


*
. This is much easier.

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

Similarly, a square root is not taken into consideration simplified if the radicand consists of a fraction.


Simplified Square Roots

A square source is taken into consideration simplified if there are

no perfect-square factors in the radicandno fountain in the radicandno square root in the denominator of a fraction

To rationalize a denominator, we use the residential property that

*
.
*
Remove common factors.
*

Simplify:

*
Simplify the denominator
*
Simplify.
*

Simplify:

*
Simplify the denominator.
*
Simplify.
*

Simplify:

*
Multiply the conjugates in the denominator.
*
Simplify the denominator.
*
We leaving the molecule in factored type to do it easier to look at for common factors ~ we have 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 carry out not square the numerator. In factored form, we deserve to see there space no common factors to remove from the numerator and also denominator.

See more: Can I Take Zyrtec And Mucinex Sinus, Mucinex And Zyrtec Interactions Checker


Simplify:

*

Elementary Algebra by OSCRiceUniversity is license is granted under a creative Commons Attribution 4.0 worldwide License, except where otherwise noted.