(i) 420 is greater than 20 from the square number 400.
∴ 420 – 20 = 400 ⇒ \(\sqrt{400}\) = 20
∵ Something is to be added to 420.
So we will think from 20 to 21.
∵ (21)2 = 441
∴ 441 – 420 = 21 should be added.
(ii) we see that 2000 is more than 64 from a square numbers 1936
∴ 2000 – 64= 1936
\(\sqrt{1936}\) = 44
∴ To get a perfect square 44 + 1 = 45
∵ (45)2 = 2025
∴ 2025 – 2000 = 25 should be added.
(iii) We see that 837 is more than 53 from a perfect square number.
∴ 837 – 53 = 784
∵ \(\sqrt{784}\) = 28
To get a perfect square = 28 + 1 = 29
∵ (29)2 = 841
∴ 841 – 837 = 4 should be added
(iv) We see that 3500 is more than 19 from a perfect square number
∴ 3500 – 19 = 3481
∵\(\sqrt{3481}\) = 59
To get a perfect square = 59 + 1 = 60,
∵ (60)2 = 3600
∴ 3600 – 3500 = 100 should be added.