A Square and a Cube Class 8 MCQ

A Square and a Cube Class 8 MCQ

A Square and a Cube Class 8 MCQ

Question 1.

Consider the given set of numbers. {576, 615, 784, 961, 972, 1024, 1225, 1396} Which of these options correctly classifies the numbers as perfect and non- perfect square numbers?

(a)

(b)

(c)

(d)

Solution:

(c)

Question 2.

Which of these is the digit at unit’s place in square of 1458?

(a) 1

(b) 4

(c) 5

(d) 6

Solution:

(b) 4

Question 3.

The digit at unit’s place of a square of a number is 2 more than the digit at unit place of that number. Which of these can be the digit at the unit’s place of the square of the number?

(a)1

(b) 3

(c) 5

(d) 9

Solution:

(d) 9

Question 4.

What is the square root of 144?

(a) 6

(b) 12

(c) 24

(d) 72

Solution:

(b) 12

Question 5.

Which of these is a prime factorisation of a square number?

(a) 2 × 3 × 5 × 5

(b) 3 × 3 × 4 × 5 × 5

(c) 2 × 2 × 3 × 5 × 5 × 7 × 7

(d) 2 × 2 × 3 × 3 × 5 × 5 × 11 × 11

Solution:

(d) 2 × 2 × 3 × 3 × 5 × 5 × 11 × 11

Question 6.

The prime factorisation of an even square number is as shown.

3 × 3 × 5 × 5 × 7 × 7 × 7 × p

What is the smallest value of p?

(a) 2

(b) 4

(c) 14

(d) 28

Solution:

(d) 28

Question 7.

Is 343 a perfect cube?

(a) Yes, because 3 is in one’s place.

(b) No, because it is an odd number.

(c) No, because the sum of the digits is not a perfect cube.

(d) Yes, because all its prime factors can be grouped in triples.

Solution:

(d) Yes, because all its prime factors can be grouped in triples.

Question 8.

Consider the given set of numbers. {215, 625, 841, 1000, 1331, 2744, 12321, 27000, 35937, 64000}

Which option correctly classifies the given numbers as cube numbers and non-cube numbers?

(a) There are 6 cube numbers and 4 non-cube numbers in the given set.

(b) There are 5 cube numbers and 5 non-cube numbers in the given set.

(c) There are 4 cube numbers and 6 non-cube numbers in the given set.

(d) There are 3 cube numbers and 7 non-cube numbers in the given set.

Solution:

(c) There are 4 cube numbers and 6 non-cube numbers in the given set.

Question 9.

Which digit comes in one’s place in the cube of 17325483?

(a) 1

(b) 3

(c) 7

(d) 9

Solution:

(c) 7

Question 10.

Which digit comes in one’s place in the result of the expression (21476 + 31520 + 41305 + 50697)³?

(a) 2 because 6 + 0 + 5 + 7 = 18 and 8 × 8 × 8 = 512

(b) 2 because 2 + 3 + 4 + 5 = 14 and 4 + 4 + 4 = 12

(c) 4 because 2 + 3 + 4 + 5 = 14 and 4 × 4 × 4 = 64

(d) 4 because 6 + 0 + 5 + 7 = 18 and 8 + 8 + 8 = 24

Solution:

(a) 2 because 6 + 0 + 5 + 7 = 18 and 8 × 8 × 8 = 512

Question 11.

How many consecutive odd numbers must be added to get the sum equal to 24³?

(a) 2

(b) 4

(c) 20

(d) 24

Solution:

(d) 24

Question 12.

Which of the following expressions can be used to find the value of [(43 + 45 + 47 + 49 + 51 + 53 + 55) - (31 + 33 + 35 + 37 + 39 + 41)]?

(a) 1 × 6 × 5 + 3

(b) 1 × 6 × 5 × 3

(c) 1 × 7 × 6 + 3

(d) 1 + 7 × 6 × 3

Solution:

(d) 1 + 7 × 6 × 3

Case Study

Question 1.

Perfect Squares

(a) Which of these is not a perfect square number?

(i) 121

(ii) 196

(iii) 289

(iv) 325

(b) What is the square root of 121 ?

(c) What is the square root of 196 ?

(d) What is the square root of 289 ?

(e) What is the square root of 325 ?

(f) With what smallest number, the non-perfect square should be multiplied to make it a perfect square ?

Solution:

(a) (iv)

(b) 11

(c) 14

(d) 17

(e) not possible

(f) 13.

Question 2.

(a) The digit at unit place of a square of a number is 2 more than the digit at unit place of that number. Which of the following can be the digit at the unit place of the square of the number ?

(i) 1

(ii) 2

(iii) 5

(iv) 6

(b) Can there be some other digit(s) at the unit place of the square of the number in such a case ?

(c) If answer to (b) above is yes, write those digit(s).

(d) Are there numbers whose squares have the same unit digit as that of the number itself ?

(e) If answer to (d) above is yes, write the unit digits of such numbers.

Solution:

(a) (iv)

(b) Yes

(c) 4 and 9

(d) Yes

(e) 1, 5 and 6.

Perfect Cubes

Question 3.

Some numbers are written on the black-board :

(a) For these numbers, which of the following statements is correct ?

(i) There are 5 perfect cubes and 5 are not perfect cubes.

(ii) There are 6 perfect cubes and 4 are not perfect cubes.

(iii) There are 3 perfect cubes and 7 are not perfect cubes.

(iv) There are 4 perfect cubes and 6 are not perfect cubes.

(b) What is the cube root of 2744 ?

(c) What is the cube root of 1331 ?

(d) What is the cube root of 35937 ?

(e) What is the cube root of 64000 ?

(f) By which least number 625 should be multiplied to make it a perfect cube ?

Solution:

(a) (ii)

(b) 14

(c) 11

(d) 33

(e) 40

(f) 25