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Rationalizing the Denominator. Square roots such as 2, 3, and 5 are irrational numbers. If roots of this type appear in the denominator of a fraction, it is customary to rewrite the fraction with. a rational number in the denominator, or rationalize it.
Using Fractional Exponents to Describe Roots. The laws of exponents suggest an exponential notation for roots involving fractional exponents. For instance, applying the exponent rules to the expression a1/2, we get. Thus, a1/2 should be the number whose square is a, so we define. Similarly, we define.
• No radicals appear in the denominator of a fraction. You can use the property below to simplify radical expressions involving square roots. Using the Product Property of Square Roots
Definition of a Square Root. Square Root. If x is a number greater than or equal to zero, x represents the positive square root of x and − x represents the negative square root of x. ⋅ x x = x , ( −. )( −. ) = x. To understand the terminology of radicals, study the illustration below. radical sign. ±. positive or negative. a. radicand.
Find the square root of fraction sqrt(64/121). Tiger Algebra's step-by-step solution shows you how to find the square roots of fractions.
For example, in , which we read as “the square root of 64,” the radicand is 64. A radical, which is any term containing both a radical sign and a radicand, is a root of a quantity. For example, is a radical. In general, the square root of b is x (written as ) if and only if x 0 and x2 b.
