Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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0:50 minutes

Problem 9

Textbook Question

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number.____-√9/16

Verified step by step guidance

Identify the expression to evaluate: \(-\sqrt{\frac{9}{16}}\).

Recognize that the square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator: \(\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}}\).

Calculate the square root of the numerator: \(\sqrt{9} = 3\).

Calculate the square root of the denominator: \(\sqrt{16} = 4\).

Combine the results to express the square root of the fraction: \(\frac{3}{4}\), and apply the negative sign: \(-\frac{3}{4}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. For non-negative numbers, square roots yield real numbers, while negative numbers do not have real square roots. For example, √9 = 3, since 3² = 9, but √-1 is not a real number.

Negative Numbers and Real Numbers

Real numbers include all rational and irrational numbers, but they do not include imaginary numbers. When evaluating expressions involving square roots, if the radicand (the number under the square root) is negative, the result is not a real number. For instance, the square root of a negative number results in an imaginary number.

Fractional Expressions

A fractional expression is a ratio of two numbers, where the denominator is not zero. In the expression -√9/16, the numerator is the square root of 9, which is 3, and the denominator is 16. This results in a real number, specifically -3/16, since both components are real.