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Chapter 0: Problem 42

Evaluate the expressions, rounding your answer to four significant digits where necessary. $$ \sqrt{\frac{9}{4}} $$

Short Answer

Expert verified
The evaluated expression for \( \sqrt{\frac{9}{4}} \) is \( \frac{3}{2} \).

Step by step solution

01

Evaluate the fraction inside the square root

First, we need to evaluate the given fraction inside the square root: \( \frac{9}{4} \)
02

Simplify the fraction

In this case, the fraction \( \frac{9}{4} \) is already in its simplest form as the numerator and denominator have no common factors other than 1. So the fraction remains unchanged.
03

Evaluate the square root of the fraction

Now, we need to find the square root of the fraction \( \frac{9}{4} \). We have: \( \sqrt{\frac{9}{4}} \)
04

Apply square root property

Apply the property of the square root of a fraction: \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \). In this case, \(a = 9\) and \(b = 4\). Applying the property, we get: \( \sqrt{\frac{9}{4}} = \frac{\sqrt{9}}{\sqrt{4}} \)
05

Evaluate the square root of the numerator and denominator

Now, find the square roots of the numerator and denominator values separately: \( \sqrt{9} = 3 \) and \( \sqrt{4} = 2 \)
06

Substitute the square roots back into the expression

Now that we have the square roots of the numerator and denominator, we can substitute them back into the expression: \( \frac{\sqrt{9}}{\sqrt{4}} = \frac{3}{2} \)
07

Verify if rounding is necessary

Since the result is an exact value (a simple fraction), there is no need to round the answer to four significant digits.
08

State the final answer

The evaluated expression is: \( \sqrt{\frac{9}{4}} = \frac{3}{2} \)

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Most popular questions from this chapter

\(\left(x^{3}+1\right) \sqrt{x+1}-\left(x^{3}+1\right)^{2} \sqrt{x+1}\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}-x-3=0\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{4 \times 2}{\left(\frac{2}{3}\right)}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(4+\frac{5}{9}\)

Find all possible real solutions of each equation \(y^{3}+64=0\)
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