Question

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

Explanation:

Step1: Calculate inside the parentheses

First, calculate \(4^2 - 8\). We know that \(4^2 = 16\), so \(16 - 8 = 8\).

Step2: Calculate the product inside the cube root

Next, calculate \(8\times8\) (since the result from Step 1 is 8). \(8\times8 = 64\).

Step3: Simplify the cube root

Now, find the cube root of 64? Wait, no, wait. Wait, the expression is \(\sqrt[3]{8\times(4^2 - 8)}\). Wait, Step 1: \(4^2 - 8 = 16 - 8 = 8\). Step 2: \(8\times8 = 64\)? Wait, no, 8 times 8 is 64? Wait, no, 8 times (4² - 8) is 8 times 8, which is 64? Wait, but the cube root of 64 is not an integer. Wait, maybe I made a mistake. Wait, wait, 4² is 16, 16 - 8 is 8. Then 8 times 8 is 64? Wait, no, the original expression is \(\sqrt[3]{8\times(4^2 - 8)}\). Wait, 8 times (16 - 8) is 8 times 8, which is 64. Then the cube root of 64 is \(\sqrt[3]{64}\)? Wait, no, 4 cubed is 64? Wait, 4³ is 64? Wait, 4×4×4 is 64? Yes, 4×4=16, 16×4=64. So \(\sqrt[3]{64}=4\). Wait, no, wait, 8×(4² - 8) = 8×(16 - 8) = 8×8 = 64. Then \(\sqrt[3]{64}=4\)? Wait, no, 4³ is 64, so cube root of 64 is 4. Then the original expression is 8.3 - 4? Wait, no, wait, the expression is \(8.3 - \sqrt[3]{8\times(4^2 - 8)}\). Let's re - do:

Step 1: Calculate the exponent and subtraction inside the parentheses: \(4^2=16\), \(16 - 8 = 8\).

Step 2: Calculate the product inside the cube root: \(8\times8 = 64\).

Step 3: Calculate the cube root: \(\sqrt[3]{64}=4\) (because \(4\times4\times4 = 64\)).

Step 4: Subtract from 8.3: \(8.3-4 = 4.3\).

Wait, but wait, 8×(4² - 8) is 8×8 = 64? Wait, no, 8×(4² - 8)=8×(16 - 8)=8×8 = 64. Then \(\sqrt[3]{64}=4\). Then 8.3 - 4 = 4.3.

Wait, but let's check again. 4 squared is 16, 16 minus 8 is 8. 8 times 8 is 64. Cube root of 64 is 4 (since 4^3 = 64). Then 8.3 minus 4 is 4.3.

Answer:

\(4.3\)