Square Root Cube
1. **Stating the problem:**
Find the square roots of the numbers 324 and 529.
2. **Square root of 324:**
Since $324 = 18^2$, the square roots are $\pm 18$.
3. **Square root of 529:**
Since $529 = 23^2$, the square roots are $\pm 23$.
---
4. **Evaluate the cube of the given numbers:**
i) $5^3 = 5 \times 5 \times 5 = 125$
ii) $(-17)^3 = (-17) \times (-17) \times (-17) = -4913$
iii) $(-2.4)^3 = (-2.4) \times (-2.4) \times (-2.4) = -13.824$
---
5. **Evaluate the cube roots:**
i) $\sqrt[3]{-15.625} = -2.5$ because $(-2.5)^3 = -15.625$
ii) $\sqrt[3]{2744} = 14$ because $14^3 = 2744$
iii) $\sqrt[3]{-238.328} = -6.2$ because $(-6.2)^3 = -238.328$
**Final answers:**
- Square roots of 324: $\pm 18$
- Square roots of 529: $\pm 23$
- $5^3 = 125$
- $(-17)^3 = -4913$
- $(-2.4)^3 = -13.824$
- $\sqrt[3]{-15.625} = -2.5$
- $\sqrt[3]{2744} = 14$
- $\sqrt[3]{-238.328} = -6.2$