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in Square and Square Root by (49.3k points)
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What is to be added in the following numbers so that they become perfect squares ?

(i) 420
(ii) 2000
(iii) 837
(iv) 3500

1 Answer

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Best answer

(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.

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