Question

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

Answer 1

we should x 3 and after multiplying by 3 the number becomes 6084 and its square root is 78

Answer 2

Solution :

Resolving 2028 into product of prime,

we get ,

2 | 2028
________
2 | 1014
________
3 | 507
________
13 | 169
________
*******13

2028 = 2 × 2 × 3 × 13 × 13

= ( 2 × 2 ) × 3 × ( 13 × 13 )

We see that 2 , 13 exist in pairs .

while 3 is alone .

So , we should multiply the given

number by 3 to get a perfect square.

Therefore ,

the perfect square so obtained is

2028 × 3 = 6084

Now ,

Square root of 6084

= √6084

= √( 2 × 2 )( 3 × 3 )( 13 × 13 )

= 2 × 3 × 13

= 78

Therefore ,

√6084 = 78

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