Question

Evaluate :
$\left(i\right)3\sqrt{4^3\times 6^3}\left(ii\right)3\sqrt{8\times 17\times 17\times 17}\left(iii\right)3\sqrt{700\times 2\times 49\times 5}\left(iv\right)1253\sqrt{a^6}-3\sqrt{125a^6}$

Answer 1

$\left(i\right)3\sqrt{4^3\times 6^3}=4\times 6=24\left(ii\right)3\sqrt{8\times 17\times 17\times 17}=3\sqrt{2\times 2\times 2\times 17\times 17\times 17}=3\sqrt{2^3\times {17}^3}=2\times 17=34\left(iii\right)3\sqrt{700\times 2\times 49\times 5}=3\sqrt{2\times 2\times 5\times 5\times 7\times 2\times 7\times 7\times 5}=3\sqrt{2^3\times 5^3\times 7^3}=2\times 5\times 7=70\left(iv\right)1253\sqrt{a^6}-3\sqrt{125a^6}=1253\sqrt{a^2\times a^2\times a^2}=-3\sqrt{5\times 5\times 5\times a^2\times a^2\times a^2}=1253\sqrt{{\left(a^2\right)}^3}-3\sqrt{5^3\times {\left(a^2\right)}^3}=125a^2-5a^2=120a^2$