Question

Find the smallest natural number by which 2178 should be multiplied to make it a perfect square. Write the square root of the resulting number

Answer 1

Answer:

I hope it will help you :)

Answer 2

Given,

The main number = 2178

To find,

The smallest natural number that should be multiplied with the main number in order to make it a perfect square.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

First of all, we need do the prime factorization of the given number.

Prime factorization :

2178 = 2 × 3 × 3 × 11 × 11

Now, if the number is a perfect square then the total number of each unique digit should be 2n. (n is an positive integer and ≠0)

Now,

Total number of digit 3 = 2 [Satisfies 2n, where n = 1]

Total number of digit 11 = 2 [Satisfies 2n, where n = 1]

Total number of digit 2 = 1 [Doesn't satisfy 2n]

Here, we need another 2, which will satisfy the 2n criteria, where n is 1.

So, the final product = 2×2×3×3×11×11 (Each unique digits are 2n in amount.)

= 4356

= Perfect square

Square root of the above perfect square = √4356 = 66

Hence, the square root of the resulting number is 66