Multiply 6561 by the smallest number so that the product is a perfect cube
Solution : Prime factors of `137592 = 2^3 xx 3^3 xx 7^3 xx 13` Show Performing prime factorization of 6561, we get 6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 6561 = (3 × 3 × 3) × (3 × 3 × 3) × 3 × 3 After grouping of the equal factors in 3’s, it’s seen that 3 × 3 is left ungrouped in 3’s. In order to complete it in a triplet, we should multiply it by 3. Hence, required smallest number = 3 and cube root of the product = 3 × 3 × 3 = 27 Toc: Cover What is the perfect cube of 6561?Complete step-by-step solution:
In order to make those two 3's a triplet, we will multiply 6561 by a 3. This will result in another triplet and 6561 will be a perfect cube.
Is 6591 a perfect cube?Answer. So, as we know that cube is multiplying a number by itself three times, we have 13. As 3 is left alone we will square it and multiply it by 6591. the answer is 59319.
Is 36000 is a perfect cube?1 Answer. ∴ 36000 is not a perfect cube.
Why 216 is a perfect cube?Transcript. Ex 7.1, 1 Which of the following numbers are not perfect cubes? (i) 216Doing Prime factorization of 216 We see that 216 = 2 × 2 × 2 × 3 × 3 × 3 Since 2 & 3 occur in triplets, ∴ 216 is a perfect cube.
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