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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Simplifying Square Roots That Contain Whole Numbers

To make it easier to work with an algebraic expression, we often simplify it. For example, you have simplified expressions as follows:

â€¢ 5(x - 4) + 2x = 7x - 20

â€¢

To simplify a square-root radical, we examine the factors of the radicand.

If any of those factors are perfect squares, we rewrite the radical so there are no perfect square factors under the radical sign.

To do this, we use the Multiplication Property of Square Roots.

We will learn two methods for simplifying square-root radicals.

To see how each method works, letâ€™s s simplify

â€¢ Method 1 Use Perfect Square Factors

Identify perfect square factors of 600.

The numbers 4, 25, and 100 are each perfect square factors of 600.

Using those factors, we can write in several ways:

 The factorization 100 Â· 6 contains 100, the largest perfect square that is a factor of 600. So we use that form. Use the Multiplication Property of Square Roots to write as the product of two radicals. Simplify
Thus, in simplified form,

Note:

Here is another way to use perfect squares to simplify

 â€¢ Method 2 Use Prime Factors If you have trouble finding a perfect square factor of the radicand, write its prime factorization. Then, group the factors to form perfect squares. Write the prime factorization of 600. Group pairs of factors to form perfect squares. Write as a product of three radicals. Simplify and simplify
Thus, in simplified form,