Question

find the smallest number by which 1250 must be multiplied to get a perfect square. also find the square root of the number so obtained.​

Answer 1

2 is the smallest number by which 1250 must be multiplied to get a perfect square..

The square root of the number obtained=√625=25

Answer 2

Answer:

The smallest number to be multiplied by which 1250 must be multiplied to get a perfect square = 2

The square root of the number thus obtained  = 50

Step-by-step explanation:

Given number is 1250

To find,

The smallest number is to be multiplied by which 1250 to get a perfect square.

Solution:

Given number is 1250

The prime factorization of 1250 is

1250 = 2 ×5×5×5×5

= 2 × 5⁴

From the prime factorization 2 × 5⁴, we get 5⁴ is a perfect square

Hence to make 2 × 5⁴ a perfect square, we need to multiply 2 × 5⁴ by 2,

Then prime factorization becomes 2² × 5⁴, a perfect square

∴ The smallest number to be multiplied by which 1250 must be multiplied to get a perfect square = 2

The perfect square is thus obtained by multiplying with 2 = 1250×2 = 2500

The square root of 2500 = 50

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