Question

2028 - By which smallest number this number should be multiplied, so that the result becomes a perfect square? Find the square root of the result obtained.

Answer 1

Hey Mate !!

The prime Factorization of 2028 is,

2028 = 2 × 2 × 3 × 13 × 13

Here, We can see the number 2 is paired 1 time and 13 is paired 1 time while 3 is remained unpaired.

When we multiply 2028 with 3. The product is 2028 × 3 = 6084

The prime Factorization of 6084 is

6084 = 2 × 2 × 3 × 3 × 13 × 13

All numbers are paired. Hence, 6084 is a perfect square. The Square root is :

= 2 × 3 × 13

= 6 × 13

= 78

Therefore,

The Square root of 6084 is 78

Answer 2

Heya!

Here is yr answer.....

Let us prime factorize 2028 ----

2028 = 2 × 2 × 3 × 13 × 13

Here, both 2 and 13 are paired.... bt, the prime factor '3' is left alone!

So, now multiply 2028 with three ---

2028 × 3 = 6084

Now, prime factorize 6084 ----

6084 = 2 × 2 × 3 × 3 × 13 × 13

Since, all the nos. are paired..... 6084 is perfect square!!

Therefore, 2028 should be multiplied by 3 to get perfect square....

Square root of 2028 ------

= √2028

= 78

The square root of 2028 is 78

Hope it helps.....

:)