Question

Find the nearest integer to the square root of the following numbers. 

(i) 232 

(ii) 600 

(iii) 728 

(iv) 824 

(v) 1729

Answer 1

(i) 232 

232 lies between 225 = (15²) and 256 = ( 16²) 

232 – 225 = 7 and 256 – 225 = 31 

7 < 31 

∴ √232 is nearest to 15. 

 (ii) 600

600 lies between 576 = (24²) and 625 = (25²) 

600 – 576 = 24 and 625 – 600 = 25 

24 < 25 

∴ √600 is nearest to 24. 

(iii) 728

728 lies between two square 

No. 676 and 729 

676 = 26 × 26 

∴√676 = 26 

and 729 = 27 × 27 

∴ √729 = 27 

Now 728 is nearer to 729. 

∴√728 is 27 

(iv) 824

824 lies between 784=(28²) and 841 =(29²) 

824 – 784 = 40 and 841 – 824= 17 

17 < 40 

∴ √824 is nearest to 29. 

(v) 1729

1729 lies between 1681 = (41²) and 1764 = (42²) 

1729 – 1681 =48 and 1764- 1729 = 35 

35 < 48 

∴ √1729 is nearest to 42.