Olympiad Test: Cube And Cube Roots - 1


20 Questions MCQ Test Mathematical Olympiad Class 8 | Olympiad Test: Cube And Cube Roots - 1


Description
Attempt Olympiad Test: Cube And Cube Roots - 1 | 20 questions in 40 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study Mathematical Olympiad Class 8 for Class 8 Exam | Download free PDF with solutions
QUESTION: 1

Which of the following numbers is a perfect cube?

Solution:

Here 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 243 = 3 × 3× 3 × 3 × 3
1331 = 11 × 11 × 11 
250 = 2 × 5 × 5 × 5
Clearly 1331 is a perfect cube.

QUESTION: 2

What will be the volume of a cube having edge length 12m? (in m3)

Solution:

Volume of cube = (12)3 = 1728 m3

QUESTION: 3

What is the smallest number by which 576 is divided that quotient is a perfect cube?

Solution:

We have 
576 = 2 × 2 × 2 × 3 × 2 × 2 × 2 × 3
∴ 576 should be divided by 9, to get a prefect cube. 

QUESTION: 4

If, 13 + 23 + 33 = (1 + 2 + 3)2, 13 + 23 + 33 + 43 = (1 + 2 + 3 + 4)2, then, 13 + 23 + 33 + 43 + 53 + 63 + 73

Solution:


= 784.

QUESTION: 5

​Observing the pattern 13 + 23 + 33 = (1 + 2 + 3)2, 13 + 23 + 33 + 43 = (1 + 2 + 3 + 4)2 , Find the sum: 

Solution:

13 + 23 + 33 + …… + 9= (1 + 2 + 3 …… + 9)2
⇒ (13 + 33 + 53 + 73 + 93) + 23 (13 + 23
+ 33 + 43)
= (45)2 = 2025
⇒ x + 23 (1 + 2 + 3 + 4)2 = 2025
⇒ x = 2025 – 8 × 100 = 1225 

QUESTION: 6

​Simplify : 

Solution:

Here 122 + 162 = 400

QUESTION: 7

Simplify : 

Solution:

QUESTION: 8

​A natural number is of the form (3n + 2). Its cube will be of the form :

Solution:

(3n + 2)3 = 27n3 + 8 + 3 × 3n × 2(3n + 2)
= 27n3 + 8 + 18n (3n + 2)
= 27n3 + 54n2 + 36n + 8
= 3 (9n3 + 18n2 + 12n + 2) + 2
= 3n + 2

QUESTION: 9

A rational number, p < 1, then,

Solution:

If, 0 < p < 1,
then, p3  < p.

QUESTION: 10

A real number ‘p’ is such that p > 1, then

Solution:

If,       p > 1
then,  p – 1 > 0
∴   p3 > p

QUESTION: 11

Three numbers are in ratio 2 : 3 : 4 and sum of their cubes is 2673. The sum of these numbers are.

Solution:

Given (2k)3 + (3k)3 + (4k)3 = 2763
⇒ 99 k3 = 2763
⇒ k3 = 27
⇒ k = 3
∴ Numbers are 6, 9, 12.
∴ Their sum = 6 + 9 + 12 = 27

QUESTION: 12

 = ?  

Solution:

QUESTION: 13

​Simplify : 

Solution:

We have 

QUESTION: 14

Which of the following is not a perfect cube?

Solution:

513 is not a perfect cube.

QUESTION: 15

The length of edge of a cube whose volume is 74.088 m3.

Solution:

4.2m = (74.088m3)1/3

QUESTION: 16

What is the smallest number by which 3087 may be multiplied so that the product is a perfect cube?

Solution:

Here 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73.
∴ 3087 has two 3 as its factors, but one 3, is short to make 3087, a perfect cube.
∴ 3 should be multiplied to 3087 to produce a perfect cube.

QUESTION: 17

What is the smallest number by which 8788 must be divided so that the duotient is a perfect cube?

Solution:

8788 = 2 × 2 × 13 × 13 × 13.
∴ 8788 should be divided by (2 × 2), i.e., 4 to produce quotient as a perfect cube. 

QUESTION: 18

What is the smallest number by which 392 may be divided so that the duotient is a perfect cube?

Solution:

392 = 2 × 2 × 2  × 7 × 7
∴ 392 should be divided by (7 × 7), i.e., 49 to produce quotient, i.e., 8 as a perfect cube. 

QUESTION: 19

Which of the following is a cube of odd numbers?

Solution:

2197 = 133.
∴ The number, i.e., 2197 is odd.
∴ Its cube root should be odd. 

QUESTION: 20

Which of the following is a cube of even numbers?

Solution:

∴ 1278 is even
∴ Its cube root should be even.

Use Code STAYHOME200 and get INR 200 additional OFF
Use Coupon Code