Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)

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Identify the expression given: $\sqrt{\frac{121}{4}}$. This is a square root of a fraction.

Recall the property of square roots that allows you to separate the root of a fraction into the root of the numerator over the root of the denominator: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.

Apply this property to the expression: $\sqrt{\frac{121}{4}} = \frac{\sqrt{121}}{\sqrt{4}}$.

Simplify the square roots of the numerator and denominator separately: $\sqrt{121}$ and $\sqrt{4}$.

Write the simplified expression as a fraction of the simplified roots: $\frac{\sqrt{121}}{\sqrt{4}}$.

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Quotient Rule for Radicals

The quotient rule for radicals states that the square root of a quotient is equal to the quotient of the square roots, i.e., √(a/b) = √a / √b, provided b ≠ 0. This rule allows simplification of expressions involving roots of fractions by separating numerator and denominator.

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Simplifying square roots involves finding the prime factors or perfect squares within the radicand to rewrite the root in simplest form. For example, √121 = 11 because 121 is a perfect square, which helps in reducing expressions to their simplest terms.

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Understanding fractions is essential when working with radicals in quotient form. Recognizing that a fraction like 121/4 can be expressed as (121)/(4) helps apply the quotient rule correctly and simplifies the expression by dealing with numerator and denominator separately.

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