Question

Which of following numbers must be multiplied to 392 to get a perfect cube??

Answer 1

Step-by-step explanation:

if we do the prime factorisation of 392 we get:

2×2×2×7

so 2×2×2 makes a cubic pair but 7 is left out so if we multiply 392 by 7×7 ...7 will also form a cubic pair hence 7 is the no.

Answer 2

Complete question with options:

Which of following numbers must be multiplied to 392 to get a perfect cube?

(a) 2 (b) 3 (c) 4 (d) 7

The smallest natural number by which 392 must be multiplied to make it a perfect cube is 7.

Among the given options option (d) 7 is correct.

Hence, all the other given options (a) 2 (b) 3 (c) 4 is incorrect.

Concept used:

In the prime factorization of a perfect cube every prime factor occurs 3 times.

To determine whether a number is a perfect cube or not proceed as follows:

1. Find the prime factors of the given number.

2. Make a pair of 3 equal prime factors.

3. If a pair contains only 1 or two equal prime factors then a given number is not a perfect cube otherwise it is a perfect cube.

Given:

Number - 392

To find:

The number by which 392 must be multiplied to make it a perfect cube.

Solution:

Step1 : Write the prime factors of 392:

Prime factors of 392 = 2 × 2 × 2 × 7 × 7    

Step 2 : Make a pair of tripelts:

392 × 7 = (2 × 2 × 2) × 7 × 7

Here, two 7s are left which are not in a triplet.

To make 392 a cube, one more 7 is required. so, we multiply 392 by 7 to make it a perfect cube.

392 × 7 = (2 × 2 × 2) × (7 × 7 × 7)

2744 is a perfect cube.

Hence, the smallest natural number by which 392 should be multiplied to make it a perfect cube is 7.

Learn more on Brainly:

Question 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100

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Question 5 For each of the following numbers, find the

smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768

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