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Chapter 0: Problem 41

Evaluate the expressions, rounding your answer to four significant digits where necessary. $$ \sqrt{\frac{16}{9}} $$

Short Answer

Expert verified
The evaluated expression is \(\frac{4}{3}\), and since it is an exact answer, no rounding is needed.

Step by step solution

01

Identify the numerator and denominator of the fraction

In the given expression \(\sqrt{\frac{16}{9}}\), the numerator is 16 and the denominator is 9.
02

Take the square root of the numerator and denominator

We need to find the square roots of both the numerator (16) and the denominator (9). The square root of 16 is 4 and the square root of 9 is 3. So we get: \[ \sqrt{16} = 4 \\ \sqrt{9} = 3 \]
03

Divide the square root of the numerator by the square root of the denominator

Now, we need to divide the square root of the numerator (4) by the square root of the denominator (3). This gives us: \[ \frac{4}{3} \]
04

Round the answer to four significant digits if necessary

Since the result obtained is an exact answer, there is no need to round it to four significant digits. Therefore, the final answer is: \[ \frac{4}{3} \]

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(\frac{1+4}{100}\right)^{-3}\)

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

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(3\left(\frac{1}{9}-\left(\frac{2}{3}\right)^{2}\right)^{2}+1\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(1-\left(-\frac{1}{2}\right)^{2}\right)^{2}+1\)

\(10 x\left(x^{2}+1\right)^{4}\left(x^{3}+1\right)^{5}+15 x^{2}\left(x^{2}+1\right)^{5}\left(x^{3}+1\right)^{4}\)
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