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) 15² = 225 < 232 < 16² = 256

Here, 232 is nearer to 225.

Hence, the nearest integer tois 15.

(ii) 24² = 576 < 600 < 25² = 625

Here, 600 is nearer to 576.

Hence, the nearest integer tois 24.

(iii) 26² = 676 < 728 < 27² = 729

Here, 728 is nearer to 729.

Hence, the nearest integer tois 27.

(iv) 28² = 784 < 824 < 29² = 841

Here, 824 is nearer to 841.

Hence, the nearest integer tois 29.

(v) 41² = 1691 < 1729 < 42² = 1764

Here, 1729 is nearer to 1764.

Hence, the nearest integer tois 42.