Question

Find each square root. See Example 1. $$ -\sqrt{\frac{49}{36}} $$

   Find each square root. See Example 1.
$$
-\sqrt{\frac{49}{36}}
$$

Trigonometry

David I. Schneider;… 12th Edition

Chapter 0, Problem 22

Instant Answer

Solved by Expert Mukesh Devi

02/18/2023

Step 1

According to the rule of radicals, the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator, when the denominator is not equal to zero. So, we can rewrite the expression as Show more…

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Find each square root. See Example 1. $$ -\sqrt{\frac{49}{36}} $$

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Key Concepts

Negative Sign in Expressions

The negative sign placed outside of the square root affects the entire value after the radical has been simplified. It is applied as an external multiplication, ensuring that the final result has the correct sign according to the rules of algebra.

Square Root

A square root of a number is a value that, when multiplied by itself, equals the original number. This concept is fundamental in algebra and is used to reverse the process of squaring a number, allowing for the simplification of expressions and solving of equations.

Radical Simplification

Simplifying radicals involves expressing the square root (or other roots) in a form that is easier to interpret or further manipulate. This frequently includes identifying perfect square factors within the radicand (the expression under the radical) and rewriting the square root in terms of these factors.

Square Root of a Fraction

The property of square roots with fractions states that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator, provided that both parts are nonnegative. This allows one to simplify each component of the fraction independently, making complex radicals more manageable.

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