Page 71 - Maths Skills - 8

Cubes and Cube Roots 69

Answer the following questions on the basis of the Reason (R): The cube of an odd natural number
above data. is odd.
Q. 2. Assertion (A): 2744 is not a perfect cube and its
3
1. Evaluate: ( 125 343 ) cube root is an odd number.
2. Cube root of 729 is 9, state whether the given
statement is true or false. Reason (R): The cube of an even natural number
is even.
3. Find the value of x in the following:
x – 12 = –1343 Q. 3. Assertion (A): 3 1728 = 3 1728 = 12
3
729 3 729 9
4. Find the cube of –(0.008)
Reason (R): For any two integers p and q, we

E. Assertion-Reason Based Questions p 3 p
Directions for Questions 1 to 3: In each of the have 3 q = 3 q , where q ≠ 0
questions given below, there are two statements
marked as Assertion (A) and Reason (R). Mark your
answer as per the codes provided below: SUBJECTIVE TYPE QUESTIONS
(a) Both A and R are true and R is the correct F. Solve the following word problems
explanation of A. 1. Find the smallest number by which 6,125 should

(b) Both A and R are true but R is not the correct be multiplied to make it perfect cube.
explanation of A. 2. Find the smallest number by which 250 should
(c) A is true but R is false. be divided to make it a perfect cube.
(d) A is false but R is true. 3. Three numbers are in the ratio 2:3:5. The sum of

Q. 1. Assertion (A): 19683 is a perfect cube and its their cubes is 54,880. Find the numbers.
cube roots is an odd number. 4. Two numbers are in ratio 2:3. The difference of
their cubes is 9,728. Find the numbers.

HOTS

1. The volume of a cubical box is 13.824 cubic metres. Find the length of each side of the box.
2. Find the smallest number that must be subtracted from 682 to make it a perfect cube.

3. Find the cube root of the following.
(i) 0.064 (ii) 0.000216 (iii) − 2 10
27

Word Stock
Cube Cube Root Pattern Triplet Consecutive