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

QUESTION
 

Evaluate the following:

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{25times 25}right}^3

                             =25^3

                             =25times 25times 25=15625 left{{sqrt{25times 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{17times 17} right )^3=17^3=17times 17times 17=4913

 

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