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Mathematics

Evaluate [(122+52)12]3\Big[(12^2 + 5^2)^{\dfrac{1}{2}}\Big]^3

Cube & Cube Roots

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Answer

[(122+52)12]3=[(144+25)12]3=[(169)12]3=[(132)12]3=[(13)22]3=[(13)]3=13×13×13=2197\Big[(12^2 + 5^2)^{\dfrac{1}{2}}\Big]^3\\[1em] = \Big[(144 + 25)^{\dfrac{1}{2}}\Big]^3\\[1em] = \Big[(169)^{\dfrac{1}{2}}\Big]^3\\[1em] = \Big[(13^2)^{\dfrac{1}{2}}\Big]^3\\[1em] = \Big[(13)^{\dfrac{2}{2}}\Big]^3\\[1em] = [(13)]^3\\[1em] = 13 \times 13 \times 13\\[1em] = 2197

Hence, [(122+52)12]3=2197\Big[(12^2 + 5^2)^{\dfrac{1}{2}}\Big]^3 = 2197

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