Maths / Cube and Cube Roots / Cube Root by Prime Factorisation

QUESTION

Evaluate the following:

$\dpi{120} \fn_jvn \large (i)\left \{ (24^2+7^2)^{1/2} \right \}^3\;(ii)\left \{ \sqrt{15^2+8^2} \right \}^3$

EXPLANATION
Explain TypeExplanation Content
Text

(i) We have

$(i)\left \{ (24^2+7^2)^{1/2} \right \}3=\left\{ (576+49)^{1/2}\right\}^3$

$=\left\{\sqrt{625}\right\}$

$=\left\{\sqrt{25\times 25}\right\}^3$

$=25^3$

$=25\times 25\times 25=15625 \left\{{\sqrt{25\times 25}=25 \right\} }$

(ii) We have,

$(ii)\left \{ \sqrt{15^2+8^2} \right \}^3=\left\{\sqrt{225+64}\right\}$

$=\left\(\sqrt{289}\right\)^3=\left\(\sqrt{17\times 17} \right\ )^3=17^3=17\times 17\times 17=4913$

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