Ex.6.3 Q1 Squares and Square Roots - NCERT Maths Class 8

Go back to  'Ex.6.3'

Question

What could be the possible one’s digits of the square root of each of the following numbers?

(i) \( 9801\)

(ii) \( 99856\)

(iii) \( 998001\)

(iv) \(657666025\)

Text Solution

What is known?

Square of numbers.

What is unknown?

Unit digit of square root.

Reasoning:

If the number ends with \(1\), then the one’s digit of the square root of that number may be \(1 \) or \(9\)

If number ends with \(6\), the one’s digit of the square root of that number may be \(4\) or \(6.\)

If number ends with \(5\), the one’s digit of square root of that number will be \( 5\). (Page \(100\) of Grade \(8\)  NCERT Book)

Steps :

(i) \(9801\)

Since the number ends with \(1\), the one’s digit of the square root may be \( 1\) or \( 9.\)

(ii) \(99856\)

Since the number ends with \( 6\), the one’s digit of the square root may be \(4\) or \(6.\)

(iii) \(998001\)

Since the number ends with \(1\), the one’s digit of the square root may be \(1\) or \(9\).

(iv) \(657666025\)

Since the number ends with \(5,\) the one’s digit of the square root will be \(5.\)