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Chapter 0: Problem 52

Evaluate the expressions, rounding your answer to four significant digits where necessary. $$ \sqrt[3]{8 \times 64} $$

Short Answer

Expert verified
\(\sqrt[3]{8 \times 64} = 8\)

Step by step solution

01

Identify the terms inside the cube root

We are given the expression \(\sqrt[3]{8 \times 64}\) and need to evaluate its value. The terms inside the cube root are 8 and 64.
02

Compute the product inside the cube root

We need to multiply the terms within the cube root. Thus, \(8 \times 64 = 512\)
03

Find the cube root of the product

Now, we will find the cube root of the product, which is 512. The cube root of a number is the value that, when multiplied by itself three times, gives that number. In this case, \(\sqrt[3]{512} = 8\) This is because \(8 \times 8 \times 8 = 512\).
04

Write the final answer

After evaluating the expression, we got that \(\sqrt[3]{8 \times 64} = 8\). Since our answer is a whole number, there is no need to round it to four significant digits. So, the final answer is: \( \sqrt[3]{8 \times 64} = 8 \)

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