1.1.3 Square Roots Key Objectives • Estimate square roots. • Simplify square root expressions. • Add, subtract, multiply, and divide square roots. Key Terms
• A principal root is the positive square root of a number, indicated by the radical sign. • Terms that include the square root of the same radicand are like radical terms . • Rationalizing the denominator is a method of rewriting a fraction by multiplying it by another fraction that is equivalent to 1 in order to remove radical terms from the denominator. Example 1 Estimating Square Roots Numbers such as 25 that have integer square roots are called perfect squares. Square roots of integers that are not perfect squares are irrational numbers. The value of the square root of a number that is not a perfect square can be estimated using the perfect squares greater than and less than that number.
Example 2 Simplifying Square-Root Expressions
A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator. The Product and Quotient Properties of Square Roots can be applied to simplify a square root, as well as to multiply or divide square roots.
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