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.

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. 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

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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.

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Simplify:

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