Question

find the real-number root using a calculator. round your answer to the nearest thousandth.
$sqrt6{179}$

Explanation:

Step1: Recall the formula for nth root

The nth root of a number \(a\) can be written as \(a^{\frac{1}{n}}\). So, \(\sqrt[6]{179}\) can be written as \(179^{\frac{1}{6}}\).

Step2: Calculate using a calculator

Using a calculator, we find the value of \(179^{\frac{1}{6}}\). First, we know that \(2^6 = 64\), \(3^6=729\). So the sixth root of 179 should be between 2 and 3. Using a calculator (for example, a scientific calculator), we calculate \(179^{1/6}\approx2.319\) (after rounding to the nearest thousandth).

Answer:

\(2.319\)