Question

find the cube root of 15625 by prime factorization method

Answer 1

SOLUTION

TO DETERMINE

The cube root of 15625

by prime factorisation method

EVALUATION

$\sf{ 15625\: }$

$= \sf{ 5 \times 5 \times 5 \times 5 \times 5 \times 5\: }$

$= \sf{ {5}^{3} \times {5}^{3} \: }$

$= \sf{ {(5 \times 5)}^{3} \: }$

$= \sf{ {25}^{3} \: }$

$\therefore \sf{ \: \: \sqrt[3]{15625} = 25 }$

FINAL ANSWER

$\boxed{ \sf{ \: \: \sqrt[3]{15625} = 25 } \: \: }$

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Answer 2

Step-by-step explanation:

15625

=5x5x5x5x5x5

=5³x5³

=(5x5)³

=25³

Therefore 25 is the cube root