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Mathematics

Evaluate (103−63)3(\sqrt{10^3 - 6^3})^3

Cube & Cube Roots

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Answer

(103−63)3=(1000−216)3=(784)3(\sqrt{10^3 - 6^3})^3\\[1em] = (\sqrt{1000 - 216})^3\\[1em] = (\sqrt{784})^3

Finding prime factors of 784

Evaluate 10^3 - 6^3^3. Cubes and Cube Roots, Concise Mathematics Solutions ICSE Class 8.

∴(784)3=((2×2)×(2×2)×(7×7))3=(2×2×7)3=(28)3=21952\therefore (\sqrt{784})^3 = (\sqrt{(2\times 2)\times (2\times 2)\times (7\times 7)})^3\\[1em] = (2 \times 2 \times 7)^3\\[1em] = (28)^3\\[1em] = 21952

Hence, (103−63)3=21952(\sqrt{10^3 - 6^3})^3 = 21952

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