1. A Square and A Cube – Textbook Worksheet

Multiple Choice QuestionsQ1: Cube root of the expression 1252
(a) 5
(b) 25
(c) 10
(d) 125

Q2: Which of the following is not a perfect square number?

(a) 1156
(b) 
4657
(c) 
4624
(d) 
7056

Q3: Which of these is not a perfect cube but a perfect square of a number 
(a) 729
(b) 2197
(c) -1331
(d) 169

Q4: Which of these is a perfect cube
(a) 216
(b) 392
(c) 8640
(d) 243

Q5: √0.09 is
(a) 0.3
(b) 0.03
(c) 0.9
(d) 0.33

Q6: The sum of first n odd natural numbers is
(a) n2
(b) 2n
(c) n2+1
(d) n2−1

Q7: The one’s digit of the cube of 53 is:

(a) 9
(b) 3
(c) 7
(d)  1

Q8: The volume of the cube is 5832m3 , the side is
(a) 18m
(b) 16 m
(c) 28 m
(d) 19m

Q9:A perfect square can never have the following digit in its ones place
(a) 8
(b) 4
(c) 0
(d) 1

Q10: Which of the following expressions is not a perfect cube
(a) 27 x 125 x 64
(b) 1331 x 125 x 8
(c) 15 x 8 x 25 x 9
(d) None of these

True and FalseQ1: 648 is not a perfect cube.

Q2: 999 is a perfect cube.

Q3: The square of a number is positive, so the cube of that number will also be positive.

Q4: 125×8×27 is a perfect cube.

Q5: For an integer p, p3 is always greater than p2.

Q6: 83 = 5.12

Fill in the blanks

Q1: The square of an even number is _____

Q2: The least number by which 72 be multiplied to make it a perfect cube is __________.

Q3: √4096 is ____

Q4: If 8x3=216, then x ix ____

Q5: The cube of .5 is _____

Q6: There are _________ perfect cubes between 1 and 1000.

Q7: The digit at the ones place of 233 is ____

Q8: The cube of the even natural number is ____

Find the cube roots by prime factorization method

Q1: 15625

Q2: 2744

Q3: 125/2197

Q4: 5832

Q5: 64000

Find the square roots by prime factorization method

Q1: 144

Q2: 3600

Q3: 2025

Q4: 81/256

Q5: 1024

Q6: 3844

Answer the following questions

Q1: Is 256 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Q2: What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 1801
(ii) 856
(iii) 1008001
(iv) 6577525

Q3: Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

Q4: Find the smallest number by which following number must be divided to get a perfect square. Also, find the square root of the perfect square so obtained.
(i)600
(ii)2904

Q5: Find the smallest number by which following number must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.
(i) 1008
(ii) 1280
(iii) 1875

​You can access the solutions to this Unit Test here.