Question

Корень корень из 64 в степени 3. Подробно как находить, пожалуйста.

Answer 1

$\sqrt{64^3} = \sqrt{(8^2)^3} = \sqrt{(8^3)^2} = 8^3 = 512$

$\sqrt{ \sqrt[3]{64} } = \sqrt[6]{8^2} = \sqrt[6]{(2^3)^2} = \sqrt[6]{2^6} = 2$

Answer 2

Finding the Cube Root of 64

To find the cube root of 64, we can use the following steps:

1. Understand the Cube Root: The cube root of a number is a value that, when multiplied by itself twice, gives the original number. In mathematical terms, if \(x^3 = 64\), then \(x\) is the cube root of 64.

2. Using Exponents: We can express 64 as \(64 = 4^3\). This means that the cube root of 64 is 4.

3. General Formula: The general formula for finding the cube root of a number is \(\sqrtx}\), where \(x\) is the number for which we want to find the cube root.

4. Example: Let's take another example to understand the concept. If we want to find the cube root of 8, we can express it as \(8 = 2^3\), so the cube root of 8 is 2.

5. Conclusion: Therefore, the cube root of 64 is 4.