Question

problem
tell which of these numbers is greater.
after you enter your answer press go.
a. $sqrt{6}$ b. $sqrt3{8}$

Explanation:

Step1: Calculate the approximate value of \(\sqrt{6}\)

We know that \(\sqrt{4} = 2\) and \(\sqrt{9}=3\), and \(4<6<9\), so \(\sqrt{6}\) is between \(2\) and \(3\). Using a calculator, \(\sqrt{6}\approx 2.45\).

Step2: Calculate the value of \(\sqrt[3]{8}\)

By the definition of cube - root, if \(x^{3}=a\), then \(x = \sqrt[3]{a}\). Since \(2^{3}=8\), so \(\sqrt[3]{8}=2\).

Step3: Compare the two values

We have \(\sqrt{6}\approx2.45\) and \(\sqrt[3]{8} = 2\). Since \(2.45>2\), we can conclude that \(\sqrt{6}>\sqrt[3]{8}\).

Answer:

A. \(\sqrt{6}\)