Q 1 – Which of the following is a perfect square number.
(a) 453
(b) 8657
(c) 93542
(d) 729
Q 2 – Which of 225², 97², 53² and 809² would end with digit 1.
(a) 225²
(b) 97²
(c) 53²
(d) 809²
Q 3 – What will be the number of zeros in the square of the number 7000?
(a) 3
(b) 5
(c) 6
(d) 9
Q 4 – How many natural numbers lie between 13² and 14².
(a) 24
(b) 25
(c) 26
(d) 27
Q 5 – Express the square number 5² as the sum of two consecutive integers.
(a) 12 + 13
(b) 10 + 15
(c) 9 + 16
(d) 20 + 5
Q 6 – Which of the following is not a Pythagorean triplet?
(a) 6, 8, 10
(b) 8, 15, 17
(c) 2, 5, 7
(d) 5, 12, 13
Q 7 – What could be the possible one’s digit of the no. whose square is 361?
(a) 3, 4
(b) 6, 7
(c) 1, 9
(d) 7, 8
Q 8 – The smallest number by which 75 should be multiplied so as to get a perfect square is
(a) 2
(b) 3
(c) 5
(d) 7
Q 9 – The number of digits in the square root of 78400 is ………….
(a) 1
(b) 2
(c) 3
(d) 4
Q 10 – Which of the following is the number of non-perfect square number between 17² and 18²?
(a) 613
(b) 35
(c) 70
(d) 34
Q 11 – Fill in the blanks:
- 1² = 1 then the square root of 1 is ………………..
- 8² = 64 then square root of ……………… = 8.
- The number of digits in the square root of 441 is ……………..
- The smallest 3-digit perfect square is ………………….
- If a number has 4 or 6 in the units place then, its square ends in ………………..
Q 12 – Find the perfect square numbers between 40 and 50.
Q 13 – Write each of the following numbers as difference of the square of two consecutive natural numbers.
(i) 49
(ii) 75
(iii) 125
Q 14 – Find the product of the following:
(i) 23 × 25 (ii) 41 × 43
Q 15 – Which of the following triplets are Pythagorean?
(i) (14, 48, 50) (ii) (18, 79, 82)
Q 16 – Find the square root of the following using successive subtraction of odd numbers starting from 1.
(i) 169 (ii) 81 (iii) 225
Q 17 – A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m away from the wall and the ladder just reaches the top of the wall, how high is the wall?
Q 18 – The area of a rectangular field whose length is twice its breadth is 2450 m2. Find the perimeter of the field.
Q 19 – What is the least number that must be subtracted from 3793 so as to get a perfect square? Also, find the square root of the number so obtained.
Q 20 – Show that the sum of two consecutive natural numbers is 132.
Q 21 – What would be the square root of 625 using the identity (a + b)2 = a2 + b2 + 2ab?
Q 22 – Find the square roots of 100 and 169 by the method of repeated subtraction.
Q 23 – 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.