Question 2(iv):
Explanation:
To find the value of \(\sqrt[3]{-64}\), we need to find the cube root of -64. The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
Steps to find the cube root of -64:
- Start by expressing -64 as \(-64 = -4 \times 4 \times 4 = -4 \times 4^2\)
- Rewrite -64 as \(-4 \times 4^2\) to find the cube root
- The cube root of -64 can be written as \(\sqrt[3]{-64} = \sqrt[3]{-4 \times 4^2}\)
- Break down the cube root into individual components: \(\sqrt[3]{-4} \times \sqrt[3]{4^2}\)
- The cube root of -4 is -1 since (-1) x (-1) x (-1) = -4
- The cube root of \(4^2\) is 4 since 4 x 4 x 4 = 64
- Therefore, the cube root of -64 is \(-1 \times 4 = -4\)
Hence, the cube root of -64 is -4.