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E:\Working\Focus_Learning\Math_Genius-8\Open_Files\07_Chapter_6\Chapter_6
\ 06-Jan-2025 Bharat Arora Proof-6 Reader’s Sign _______________________ Date __________

3. The cube of every ............... number is even.

4. 3 540 = ......... × 3 × 3 5 5. 3 1331 = .........
3
4913 .........
D. State whether the following statements are true (t) or False (F).

1. The cube of any odd number is even.
2. The cube of a 2-digit number may have six or more digits.

1
(
)
3. 512 3 = 8
4. The cube root of the product of a positive number and a negative number is a negative number.
5. The least number by which 648 should be divided to get a perfect cube is 2.

E. Answer the following.

1. Find the cube of the following.

(a) 17 (b) 21 (c) –101 (d) 3 (e) –3a b
2
11
2. Evaluate the following:
(a) 3 36 × 3 384 (b) 3 2592 × 3 144

3. Find the unit’s digit of the cube root of the following numbers:

(a) 226981 (b) 274625
4. Is 578 a perfect cube? If not, find the smallest natural number by which 578 must be multiplied so
that the product is a perfect cube.

.
.
3
5. Find the value of 2 197. + 3 0 008 − 3 0 125 .
6. Show that the following numbers are cubes of a rational number. Also, find the rational number
whose cubes they represent.
−3375
(a) (b) 0.238328 (c) – 0.343
6859
7. The difference of two perfect cubes is 279. If the cube root of the smaller of the two numbers is 4,
find the cube root of the larger number.
8. The school management decided to give prizes on the occasion of the Annual Day to encourage
the development of virtues like regularity, obedience, and social service amongst the students.
On the prize distribution day, it was observed that the number of students getting prizes in the
three categories was in the ratio 3 : 5 : 7, and the product of the number of students in these Case study
categories was 2835.
Based on the above information answer the following questions.

(a) Find the number of students receiving prizes in the ‘obedience’ category.
(b) Find the number of students receiving prizes in the ‘regularity’ category.
(c) Find the total number of prizes in all the three categories.
(d) If each prize cost to school management is `250, then find the total amount they spend.

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