Multiply 137592 by the smallest number so the product is a perfect cube and also find the cube
root of product.
Answers
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
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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
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 productsolution : first find prime factors of 137592.
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,23 x 33 x 72 x 13 x 7 x 132 = (2 x 3 x 7 x 13) = a perfect cube.
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,23 x 33 x 72 x 13 x 7 x 132 = (2 x 3 x 7 x 13) = a perfect cube.so, the smallest number is 7 x 132 = 1183 = and the cube root of product = X{(2 x 3 x =
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,23 x 33 x 72 x 13 x 7 x 132 = (2 x 3 x 7 x 13) = a perfect cube.so, the smallest number is 7 x 132 = 1183 = and the cube root of product = X{(2 x 3 x =7 * 13))
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,23 x 33 x 72 x 13 x 7 x 132 = (2 x 3 x 7 x 13) = a perfect cube.so, the smallest number is 7 x 132 = 1183 = and the cube root of product = X{(2 x 3 x =7 * 13))= 2 x 3 x 7 x 13 = 546
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 productsolution : first find prime factors of 137592.i.e., prime factors of 137592 = 23 x 33 x 72 x 13here it is clear that when we multiply 137592 by the number 7 x 132 we get,23 x 33 x 72 x 13 x 7 x 132 = (2 x 3 x 7 x 13) = a perfect cube.so, the smallest number is 7 x 132 = 1183 = and the cube root of product = X{(2 x 3 x =7 * 13))= 2 x 3 x 7 x 13 = 546Therefore the smallest number is 1183 and the cube root of the product is 546.