  Question

Evaluate: (1) ${4}^{\frac{1}{2}}$ (2) ${125}^{\frac{1}{3}}$ (3) ${1}^{\frac{1}{2}}$ (4) ${1}^{\frac{1}{3}}$ (5) ${100}^{\frac{1}{2}}$ (6) ${1000}^{\frac{1}{3}}$ (7) ${225}^{\frac{1}{2}}$ (8) ${512}^{\frac{1}{3}}$ (9) ${64}^{\frac{1}{2}}$ (10) ${64}^{\frac{1}{6}}$

Solution

(1) ${4}^{\frac{1}{2}}$ can be written as the square root of 4. And 4 = 2 × 2 So, square root of 4 = 2 $\therefore {4}^{\frac{1}{2}}=\sqrt{4}=2$ (2) ${125}^{\frac{1}{3}}$ can be written as the cube root of 125. And 125 = 5 × 5 × 5 So, cube root of 125 = 5 $\therefore {125}^{\frac{1}{3}}=\sqrt{125}=5$ (3) ${1}^{\frac{1}{2}}$ can be written as the square root of 1. And 1 = 1 × 1 So, square root of 1 = 1 $\therefore {1}^{\frac{1}{2}}=\sqrt{1}=1$   (4) ${1}^{\frac{1}{3}}$can be written as the cube root of 1. And 1 = 1 × 1× 1 So, cube root of 1 = 1 $\therefore {1}^{\frac{1}{3}}=\sqrt{1}=1$ (5) ${100}^{\frac{1}{2}}$ can be written as the square root of 100. And 100 = 10 × 10 So, square root of 100 = 10 $\therefore {100}^{\frac{1}{2}}=\sqrt{100}=10$ (6) ${1000}^{\frac{1}{3}}$ can be written as the cube root of 1000. And 1000 = 10 × 10 × 10 So, cube root of 1000 = 10 $\therefore {1000}^{\frac{1}{3}}=\sqrt{1000}=10$ (7) ${225}^{\frac{1}{2}}$ can be written as the square root of 225. And 225 = 15 × 15 So, square root of 225 = 15 $\therefore {225}^{\frac{1}{2}}=\sqrt{225}=15$ (8) ${512}^{\frac{1}{3}}$ can be written as the cube root of 512. And 512 = 8 × 8 × 8 So, the cube root of 512 = 8 $\therefore {512}^{\frac{1}{3}}=\sqrt{512}=8$ (9) ${64}^{\frac{1}{2}}$ can be written as the square root of 8. And 64 = 8 × 8 So the square root of 64 = 8 $\therefore {64}^{\frac{1}{2}}=\sqrt{64}=8$ (10) ${64}^{\frac{1}{6}}$ can be written as the sixth root of 64. And 64 = 2 × 2 × 2 × 2 × 2 × 2 So the sixth root of 64 = 2 $\therefore {64}^{\frac{1}{6}}=\sqrt{64}=2$ MathematicsMathematics(2013)Standard VIII

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