Evaluate: (i) 3√(4^3 x 6^3) (ii) 3√(8 x 17 x 17 x 17) (iii) 3√(700 x 2 x 49 x 5)

Question

Evaluate:

(i) \(\sqrt[3]{4^3\times6^3}\)

(ii) \(\sqrt[3]{8\times17\times17\times17}\)

(iii) \(\sqrt[3]{700\times2\times49\times5}\)

(iv) \(125\sqrt[3]{a^3}\) - \(\sqrt[3]{125a^6}\)

Answer 1

(i) \(\sqrt[3]{4^3\times6^3}\)

We have,

= \(\sqrt[3]{4^3\times6^3}\)

= \(\sqrt[3]{4^3}\times\) \(\sqrt[3]{6^3}\)

= \(4\times6\)

= 24.

(ii) \(\sqrt[3]{8\times17\times17\times17}\)

We have,

= \(\sqrt[3]{8\times17\times17\times17}\)

= \(\sqrt[3]{8\times}\) \(\sqrt[3]{17^3}\)

= \(\sqrt[3]{2^3}\times\) \(\sqrt[3]{17^3}\)

= \(2\times17 \)

= 34.

(iii) \(\sqrt[3]{700\times2\times49\times5}\)

We have,

= \(\sqrt[3]{700\times2\times49\times5}\)

Getting prime factors of numbers,

= \(\sqrt[3]{700\times2\times49\times5}\)

= \(\sqrt[3]{2\times2\times2\times5\times5\times7\times7\times5}\)

= \(\sqrt[3]{2^3\times5^3\times7^3}\)

= \(\sqrt[3]{2^3}\times\)\(\sqrt[3]{5^3}\times\) \(\sqrt[3]{7^3}\)

= 2 × 5 × 7 = 70.

(iv) \(125\sqrt[3]{a^3}\) - \(\sqrt[3]{125a^6}\)

We have,

= \(125\sqrt[3]{a^6}\) - \(\sqrt[3]{125a^6}\)

= \(125\sqrt[3]{(a^2) ^3}\) - \(\sqrt[3]{5^3(a^2)^3}\)

= \(125a^2\) - \(\sqrt[3]{5^3(a^2)^3}\)

= \(125a^2\) - \(\sqrt[3]{5^3}\times\sqrt[3]{(a^2)^3}\)

= \(125a^2\) - \(5a^2\)

= \(120a^2. \)