Sqaure, Square Roots, Cubes and Cube Roots

1. The least positive integer k for which 15k is the cube of an integer is 
          answer: 225

     2. If k is a positive integer, the smallest value of  k  such that  60k is a perfect square is
    answer: 15
     
      3.A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p
B. pq
C. pq + 27
D. -p
E. (p - q)6
answer: c

4.  n is the least possible no. such that 18n is a perfect square. m is the least no. such that 9m is a perfect square.

                         Col A : n                                  Col B : m
answer: B

5. If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
A. 2
B. 5
C. 6
D. 7
E. 14

answer: E

6. If x and y are perfect squares, then which one of the following is not necessarily a perfect square? 
A. x^2
B. xy
C. 4x
D. x+y
E. x^5

answer: D

7.Which of the following numbers is a perfect square?
A. 1266
B. 1444
C. 2022
D. 4034
E. 8122
answer: B

8. If x^(1/6) = 6, then √x^6 is ?
A. 6
B. 6√6
C. 6^6
D. 6^18
E. 6^36
answer: D

9. If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?
(A) -15
(B) -12
(C) -9
(D) 15
(E) 18
answer: C

10. The mean of (54,820)^2 and (54,822)^2 =
(A) (54,821)^2
(B) (54,821.5)^2
(C) (54,820.5)^2 
(D) (54,821)^2 + 1
(E) (54,821)^2 – 1
answer: D

11. If m^(-1) = -1/3 then m^(-2) is equal to
(A) -9
(B) -3
(C) -1/9
(D) 1/9
(E) 9
answer: D

12. If (x - 1)^2 = 400, which of the following could be the value of x - 5?
(A) 15
(B) 14
(C) -24
(D) -25
(E) -26
answer: C