Cube root of 3 + Cube root of 0.008+ Cube root of 0.064

Cube root of 3 + Cube root of 0.008+ Cube root of 0.064

The Correct Answer and Explanation is:

Let’s start by calculating each of the cube roots individually.

1. Cube root of 3
   The cube root of 3 is the number that, when multiplied by itself three times, equals 3. Mathematically, we can express this as:
   33≈1.442.\sqrt[3]{3} \approx 1.442.33​≈1.442.
2. Cube root of 0.008
   Now, the cube root of 0.008 is the number that, when cubed, equals 0.008.
   Since:
   0.0083=8×10−33=8310003=210=0.2.\sqrt[3]{0.008} = \sqrt[3]{8 \times 10^{-3}} = \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} = \frac{2}{10} = 0.2.30.008​=38×10−3​=31000​38​​=102​=0.2.
3. Cube root of 0.064
   Similarly, the cube root of 0.064 is:
   0.0643=64×10−33=64310003=410=0.4.\sqrt[3]{0.064} = \sqrt[3]{64 \times 10^{-3}} = \frac{\sqrt[3]{64}}{\sqrt[3]{1000}} = \frac{4}{10} = 0.4.30.064​=364×10−3​=31000​364​​=104​=0.4.

Now, let’s add these values together:

33+0.0083+0.0643≈1.442+0.2+0.4=2.042.\sqrt[3]{3} + \sqrt[3]{0.008} + \sqrt[3]{0.064} \approx 1.442 + 0.2 + 0.4 = 2.042.33​+30.008​+30.064​≈1.442+0.2+0.4=2.042.

So the sum of the cube roots is approximately 2.042.

Explanation:

A cube root is essentially the inverse operation of cubing a number. When you cube a number, you multiply it by itself three times. For example, cubing 2 gives 8 (since 23=82^3 = 823=8), and cubing 0.2 gives 0.008 (since 0.23=0.0080.2^3 = 0.0080.23=0.008). In the case of 3, 1.44231.442^31.4423 gives a value very close to 3.

Understanding the cube root involves knowing that it’s the value that, when raised to the third power, yields the original number. For small values like 0.008 or 0.064, the cube root often involves fractions that are easier to work with. For example, the cube root of 0.008 being 0.2 suggests that the number 0.2 multiplied by itself three times results in 0.008.

This concept is widely used in fields like physics and engineering, where relationships involving volumes, such as in determining the side length of a cube with a given volume, often require the cube root. The cube root function helps to reverse the effects of cubic scaling and is fundamental to understanding proportions in three-dimensional space.