Find the least number which must be added to each of the following numbers to make them a perfect square. Also find the square root's of the perfect square number so obtained.
$1750$

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Solution

$\begin{matrix} 41^{2} < 1750 n e x t p e r f e c t s q u a r e i s \Rightarrow 42^{2} = 1764 h e n c e, n u m b e r t o b e a d d e d i s \Rightarrow 42^{2} - 1750 = 1764 - 1750 = 14 \Rightarrow t h e r e f o r e, t h e p e r f e c t s q u a r e s o, o b t a i n e d i s 1750 + 14 = 1764 a n d i t s s q u a r e r o o t = \sqrt{1764} = 42 \end{matrix}$

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Question 5 (iii)
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

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Find the least number which must be added to each of the following numbers to make them a perfect square. Also find the square root's of the perfect square number so obtained.1750

412<1750nextperfectsquareis⇒422=1764hence,numbertobeaddedis⇒422−1750=1764−1750=14⇒therefore,theperfectsquareso,obtainedis1750+14=1764anditssquareroot=√1764=42

Find the least number which must be added to each of the following numbers to make them a perfect square. Also find the square root's of the perfect square number so obtained.
$1750$