Question

Find the least number by which the given number should be multiplied to get a perfect square number in each case find the new number where square is the resulting new number
(1) 1458
(2) 605
(3) 2028​

Answer 1

Step-by-step explanation:

1) By prime factorisation of 1458, we get

1458=2×3×3×3×3×3×3

Here, 3 are in pairs but 2 needs a pair to make 1458 a perfect square.

So, 1458 needs to be multiplied by 2 to make it a perfect square.

Thus, the number is 1458×2=2916

2916

=

2×2×3×3×3×3×3×3

=2×3×3×3

=54

Thus 2 is the required smallest whole number to make the given number a perfect square.

2) By doing factorisation of 605 we get,

5×11×115×11×11.

We can see that 55 is left unpaired therefore we will multiply 605605 by 55.

=605×5=3025=605×5=3025

30253025 is a perfect square of 5555.

Hence, 55 is the number by which 605605 must be multiplied so that the product is a perfect square.