Question

use the aleks calculator to approximate \\(\sqrt{166}\\). round your answer to the nearest hundredth. \\(\sqrt{166} \approx \square\\)

Explanation:

Step1: Recall square root concept

The square root of a number \( x \), denoted \( \sqrt{x} \), is a value \( y \) such that \( y^2 = x \). We need to find \( \sqrt{166} \) and round to the nearest hundredth.

Step2: Use calculator for approximation

Using a calculator (like ALEKS), we calculate \( \sqrt{166} \). First, we know that \( 12^2 = 144 \) and \( 13^2 = 169 \), so \( \sqrt{166} \) is between 12 and 13. Using a calculator, \( \sqrt{166} \approx 12.8841 \).

Step3: Round to nearest hundredth

To round to the nearest hundredth, we look at the thousandth place. The number is \( 12.8841 \), the digit in the thousandth place is 4, which is less than 5, so we keep the hundredth place as is. So \( 12.8841 \approx 12.88 \).

Answer:

\( 12.88 \)