Question

use the aleks calculator to approximate \\(\sqrt{165}\\). round your answer to the nearest hundredth. \\(\sqrt{165} \approx \square\\)

Explanation:

Step1: Recall square root concept

The square root of a number \( n \), denoted as \( \sqrt{n} \), is a value \( x \) such that \( x^2 = n \). For \( \sqrt{165} \), we know that \( 12^2 = 144 \) and \( 13^2 = 169 \), so \( \sqrt{165} \) is between 12 and 13.

Step2: Use calculator for approximation

Using a calculator (like ALEKS), we calculate \( \sqrt{165} \). Let's compute it: \( \sqrt{165}\approx12.84523257866513 \).

Step3: Round to nearest hundredth

To round to the nearest hundredth, we look at the thousandth place. The number is \( 12.84523257866513 \), the thousandth digit is 5. When the digit in the thousandth place is 5 or more, we round up the hundredth place. So \( 12.84 + 0.01 = 12.85 \).

Answer:

\( 12.85 \)