NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)
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Square and square root possible unit digit number
Question: 1 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
Answer:
Unit՚s digits of square of numbers are 0, 1,4, 5,6 and 9. Therefore, the possible unit՚s digits of the given numbers are:
(i) 9801
If the number ends with 1, then the one՚s digit of the square root of that number may be 1 or 9.
Therefore, one՚s digit of the square root of 9801 is either 1 or 9.
(ii) 99856
If the number ends with 6, then the one՚s digit of the square root of that number may be 4 or 6.
Therefore, one՚s digit of the square root of 99856 is either 4 or 6.
(iii) 998001
If the number ends with 1, then the one՚s digit of the square root of that number may be 1 or 9.
Therefore, one՚s digit of the square root of 998001 is either 1 or 9.
(iv) 657666025
If the number ends with 5, then the one՚s digit of the square root of that number will be 5. Therefore, the one՚s digit of the square root of 657666025 is 5.
Question: 2 Without doing any calculation find the numbers which are surely not perfect squares:
(i) 153
(ii) 257
(iii) 408
(iv) 441
Answer:
All perfect square numbers contain their unit՚s place digits 0, 1,4, 5,6 and 9.
(i) 153
Given, number 153 has its unit digit 3.
So it is not a perfect square number.
(ii) 257
Given, number 257 has its unit digit 7.
So it is not a perfect square number.
(iii) 408
Given, number 408 has its unit digit 8.
So it is not a perfect square number.
(iv) 441
Given, number 441 has its unit digit 1.
So it would be a perfect square number
Question: 3 Find the square roots of 100 and 169 by the method of repeated subtraction.
Answer:
By successive subtracting odd natural numbers from 100,
This successive subtraction is completed in 10 steps.
Therefore
By successive subtracting odd natural numbers from 169,
This successive subtraction is completed in 13 steps.
Therefore