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Question

Find: 
(i) $$\displaystyle 64^{\dfrac{1}{2}}$$    (ii) $$\displaystyle 32^{\dfrac{1}{5}}$$    (iii) $$\displaystyle 125^{\dfrac{1}{3}}$$


Solution

i) $$(64)^{\frac{1}{2}}$$

Express $$64$$ in terms of $$8$$

$$=(8^{2})^{\dfrac{1}{2}}=8^{2\times \dfrac{1}{2}}=8^{1}=8$$

ii) $$(32)^{\dfrac{1}{5}}$$

Express $$32$$ in terms of $$2$$

$$=(2^{5})^{\dfrac{1}{5}}=2^{5\times \dfrac{1}{5}}=2^{1}=2$$

iii) $$(125)^{\dfrac{1}{3}}$$

Express $$125$$ in terms of $$5$$

$$=(5^{3})^{\dfrac{1}{3}}=5^{3\times \dfrac{1}{3}}=5^{1}=5$$

Mathematics
RS Agarwal
Standard IX

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