Question

The least number that should be multiplied by 9248 to make it a perfect square is

Answer 1

Step-by-step explanation:

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Answer 2

Given:  

A number 9248.  

To Find:  

The square root of the given number.  

Solution:  

The given problem can be solved using the concepts of prime factorization.  

1. The given number is 9248.  

2. Prime factorization of a number is defined as reducing a given number into the product of prime numbers.  

For Example: 72 is written as 2 x 2 x 2 x 3 x 3.  

3. Express 9248 as the product of prime numbers,

=> 9248 = 32 x 289,  

=> 9248 = 2 x 2 x 2 x 2 x 2 x 17 x 17,

=> √(9248) = √(2 x 2 x 2 x 2 x 2 x 17 x 17),

=> √(9248) = 4 x 17 x √2 , (√(a x a) = a)

 

4. The smallest number that can be multiplied with 9248 is 2,

=> 9248 x 2 = 18496,

=> √(9248x2) = √(2 x 2 x 2 x 2 x 2 x 2 x 17 x 17),

=> √18496 = 2 x 2 x 2 x 17,

=> √18496 = 136. (It is a perfect square).

Therefore, 2 is the smallest number that is multiplied by 9248 to make it a perfect square.