Question

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
(1) 525
(i) 1750
(m) 252
(iv) 1825
(v) 6412​

Answer 1

Answer:

1)Smallest number that should be added to

525 to make it a perfect square is 4.

after adding 4, the number will become 529 whose square root is 23.

2) The smallest numbers to be added to 1750 is 14, 1750+14=1764

prime factorization of 1764, we get

√2²×3³×7²

= 2×3×7

42

√1764=42×42

3)Hence, 252 is not a perfect square.

:15'2<252<16'2

=225<252<256

the no. nearest to 252 is 256

So 256-252=4

4 should be added to 252 to be a perfect square.....

252+4=256

√256= 16×16

4) 42×42= 1764

this is smaller so will try with 43

43×43=1849

so,

1849-1825

=24

so 24 Will be added

5) nearest perfect square

80×80=6400

which is smaller.

so,

81×81=6516

so,

6561-6412=149

so the number is 149 to be added to 6412.