Question

multiply 137592 by the smallest number so that the product is perfect cube. Also find the cube root of the product

Answer 1

we have to multiply 137592 by the smallest number so that the product is perfect cube. also have to find the cube root of the product.

solution : first find prime factors of 137592.

i.e., prime factors of 137592 = 2³ × 3³ × 7² × 13

here it is clear that when we multiply 137592 by the number 7 × 13² we get,

2³ × 3³ × 7² × 13 × 7 × 13² = (2 × 3 × 7 × 13)³ ⇒a perfect cube.

so, the smallest number is 7 × 13² = 1183

and the cube root of product = ³√{(2 × 3 × 7 × 13)³}

= 2 × 3 × 7 × 13 = 546

Therefore the smallest number is 1183 and the cube root of the product is 546.

Answer 2

Step-by-step explanation:

taking LCM of 137592

LCM is (2×2×2)×(3×3×3)×7×7×13

we need 7×(13)² to make the number 137592 a perfect cube

multiply both sides by 7×13×13 = 1183

137592 × 1183 = 2×2×2×3×3×3×7×7×7×13×13×13

162771336 = 162771336

cuberoot of 162771336 is 546

So the smallest number is 1183 and cube root of this number is 546

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