Education.com
Try
Brainzy
Try
Plus

Simplifying Radicals Study Guide (page 3)

By
Updated on Aug 24, 2011

When the Radicand Contains a Fraction

The radicand cannot be a fraction. If you get rid of the denominator in the radicand, then you no longer have a fraction. This process is called rationalizing the denominator. Your strategy will be to make the denominator a perfect square. To do that, you multiply the denominator by itself.However, if you multiply the denominator of a fraction by a number, you must multiply the numerator of the fraction by the same number. Take a look at the following examples.

Example:

Make the denominator a perfect square. 

 

Take out the square roots. One is a perfect square and so is 2 · 2.

 

Example:

Make the denominator a perfect square.

The number 1 is considered a factor of all numbers. If the numerator does not contain a perfect square, then 1 will be the perfect square and will be in the numerator. Take the square root of 1 in the numerator and 3 · 3 in the denominator. The product of 2 · 3 will give you 6 for the radicand.

Example:

Make the denominator a perfect square.

Take the square roots.                                

When a Radical Is in the Denominator

When you have a radical in the denominator, the expression is not in simplest form. The expression contains a radical in the denominator. To get rid of the radical in the denominator, rationalize the denominator. In other words, make the denominator a perfect square. To do that, you need to multiply the denominator by itself.

Example:
Simplify.
The number 9 is a perfect square.

Example:
Rationalize the denominator.
Simplify.
Take the square root of 4.

Example:
Rationalize the denominator.
Simplify.
You aren't finished yet because both radicands contain perfect squares.
 
Take the square root of 4.
Finished? Not quite. You can divide 2 into 2, or cancel the 2's. 3

Adding and Subtracting Radicals

You can add and subtract radicals if the radicands are the same. For example, you can add 3√2 and 5√2 because the radicands are the same. To add or subtract radicals, you add the number in front of the radicals and leave the radicand the same.When you add 3√2 + 5√2, you add the 3 and the 5, but the radicand √2 stays the same. The answer is 8√2.

Tip

You can add or subtract radicals only when the radicand is the same. You add radicals by adding the number in front of the radicals and keeping the radicand the same. When you subtract radicals, you subtract the numbers in front of the radicals and keep the radicand the same.

Example: 2√5 + 7√5
Add the numbers in front of the radicals. 9√5

Example: 11√5 – 4√5
Subtract the numbers in front of the radicals. 7√5

Example: 4√3 + 2√5 + 6√3
You can add only the radicals that are the same. 10√3 + 2√5

Example: 5√8 + 6√8
Add the radicals. 11√8
But √8 contains a factor that is a perfect square, so you aren't finished because your answer is not in simplest form. 11√2 · 4
Take out the square root of 4. 2 · 11√2
Simplify. 22√2

View Full Article
Add your own comment