# Squares and Square Roots

16. Consider the number a5 with unit digit 5. We have (a5)2 = a(a + 1) hundred + 25. The value of 1252 is

• (A) 15635
• (B) 15625
• (C) 16525
• (D) 16535

15. Consider the number a5 with unit digit 5. We have (a5)2 = a(a + 1) hundred + 25. The value of 7952 is

• (A) 632075
• (B) 632025
• (C) 632035
• (D) 632055

14. How many non-square numbers lie between the numbers 1002 and 1012?

• (A) 201
• (B) 199
• (C) 200
• (D) 202

13. The triangular numbers are 1, 3, 6, 10, 15, . . . The sum of 4th and 5th triangular number is

• (A) 32
• (B) 42
• (C) 62
• (D) 52

12. Which of the following is the correct value of 152, as a sum of consecutive natural numbers?

• (A) 112 + 114
• (B) 113 + 114
• (C) 112 + 113
• (D) 111 + 112

11. Which one is the correct value of 11 × 13?

• (A) 132 – 1
• (B) 112 – 1
• (C) 122 – 1
• (D) 142 – 1

10. The hypotenuse of a right triangle with its legs of lengths 3x and 4x is

• (A) 5x
• (B) 7x
• (C) 16x
• (D) 25x

9. If one member of a Pythagorean triplet is 2m, then the other two members are

• (a) m, m2 + 1
• (b) m2 + 1, m2 –1
• (c) m2, m2 –1
• (d) m2, m + 1

8. The sum of first n odd natural numbers is

• (a) 2n + 1
• (b) n2
• (c) n2 – 1
• (d) n2 + 1

7. If m is the square of a natural number n, then n is

• (a) the square of m
• (b) greater than m
• (c) equal to m
• (d) √m

6. The value of 248 + √52 + √144 is

• (a) 14
• (b) 12
• (c) 16
• (d) 13

5. Given that √4096 = 64, the value of √4096 + √40.96 is

• (a) 74
• (b) 60.4
• (c) 64.4
• (d) 70.4

4. How many natural numbers are there between n2 and (n + 1)2?

• (A) 2n – 1
• (B) 2n + 1
• (C) 2n
• (D) n – 1

3. How many digits are there in the square root of 65025?

• (A) 3
• (B) 2
• (C) 4
• (D) 1

2. The least number by which 125 be multiplied to make it a perfect square is

• (A) 2
• (B) 4
• (C) 5
• (D) 6

1. The least number by which 96 be divided to make it a perfect square is

• (A) 2
• (B) 4
• (C) 5
• (D) 3