Question

evaluate. simplify your answer. 8.3 - \sqrt3{8 \times (4^2 - 8)}

Explanation:

Step1: Calculate inside the parentheses

First, calculate the expression inside the parentheses: \(4^2 - 8\). We know that \(4^2 = 16\), so \(16 - 8 = 8\).

Step2: Calculate the cube root

Next, calculate the cube root part: \(\sqrt[3]{8\times8}\) (since we found the inside of the parentheses is 8, so it's \(8\times8\) inside the cube root? Wait, no, wait. Wait, the original expression is \(8.3-\sqrt[3]{8\times(4^2 - 8)}\). Wait, no, wait, let's re - examine. Wait, the expression is \(8.3-\sqrt[3]{8\times(4^{2}-8)}\). So first, \(4^{2}=16\), then \(16 - 8 = 8\). Then \(8\times8 = 64\)? Wait, no, \(8\times(4^{2}-8)=8\times(16 - 8)=8\times8 = 64\)? Wait, no, \(8\times8 = 64\), and the cube root of 64? Wait, no, \(\sqrt[3]{64}\) is 4? Wait, no, \(4^3=64\), yes. Wait, but wait, let's do it step by step.

Wait, first, compute the value inside the cube root: \(8\times(4^{2}-8)\).

First, \(4^{2}=16\), then \(16 - 8 = 8\). Then \(8\times8 = 64\). So now we have \(\sqrt[3]{64}\). Since \(4\times4\times4 = 64\), \(\sqrt[3]{64}=4\).

Step3: Subtract from 8.3

Now, subtract this result from 8.3: \(8.3-4 = 4.3\).

Answer:

\(4.3\)