Subjects algebra

Square Root Cube

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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: $\pm 23$ - $5^3 = 125$ - $(-17)^3 = -4913$ - $(-2.4)^3 = -13.824$ - $\sqrt[3]{-15.625} = -2.5$ - $\sqrt[3]{2744} = 14$ - $\sqrt[3]{-238.328} = -6.2$