multiply 137592 by the smallest number so that the product is perfect cube. Also find the cube root of the product
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The least no. is. 1183. and it is cube root of 546.
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Answer:
137592 =2× 2 × 2 × 3 ×3 × 3 ×7 ×7 ×13
The number 7 and 13 should be multiplied once and twice respectively so that the product is a perfect cube
∴ the smallest number by which 137592 must be multiplied
= 7 × 13 × 13 = 1183
The required product = 137592 × 1183 = 2× 2 × 2 × 3 ×3 × 3 ×7 ×7 ×13 × 7 × 13 × 13
= (2³ × 3³ × 7³ ×13³)
= (2× 3× 7 ×13)³
= ∛137592 × 1183 = 2 × 3× 7× 13
= 546
Thanks : ]
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