SEBA Class 10 Maths Revision 2 Solutions – Complete Guide for Exam Preparation

Q1. Which of the following is not a perfect cube?
(i) 3757    (ii) 3375    (iii) 3332    (iv) 4096
Answer:
A perfect cube is a number which can be written as \(n^3\).

\(3375 = 15^3\), \(4096 = 16^3\)
But 3757 and 3332 are not perfect cubes.

Final Answer:
(i) 3757 and (iii) 3332

Q2. Find the cubes of the following numbers.
(i) 19    (ii) 21    (iii) 23    (iv) 27
Answer:
Cube means multiplying the number three times.

(i) \(19^3 = 6859\)
(ii) \(21^3 = 9261\)
(iii) \(23^3 = 12167\)
(iv) \(27^3 = 19683\)

Q3. Write the digit in the unit place of the cubes of the following numbers.
(i) 14    (ii) 18    (iii) 13    (iv) 27
Answer:
We only check the unit digit of the number.

(i) 14 → unit digit 4 → \(4^3 = 64\) → unit digit = 4
(ii) 18 → unit digit 8 → \(8^3 = 512\) → unit digit = 2
(iii) 13 → unit digit 3 → \(3^3 = 27\) → unit digit = 7
(iv) 27 → unit digit 7 → \(7^3 = 343\) → unit digit = 3

Q4. Find the smallest integers with which the following numbers are to be multiplied so that they become perfect cubes.
(i) 5324    (ii) 3087    (iii) 3125    (iv) 648
Answer:
For a perfect cube, powers of prime factors must be multiples of 3.

(i) \(5324 = 2^2 \times 11^3\) → multiply by 2 → \(2^3\)
Answer = 2

(ii) \(3087 = 3^2 \times 7^3\) → multiply by 3
Answer = 3

(iii) \(3125 = 5^5\) → multiply by \(5\) to make \(5^6\)
Answer = 5

(iv) \(648 = 2^3 \times 3^4\) → multiply by 3
Answer = 3

Q5. Find the smallest numbers with which the following numbers are to be divided so that they become perfect cubes.
(i) 10368    (ii) 2187    (iii) 5000    (iv) 8192
Answer:
We divide to make powers multiples of 3.

(i) \(10368 = 2^7 \times 3^4\) → divide by \(2 \times 3\)
Answer = 6

(ii) \(2187 = 3^7\) → divide by \(3\)
Answer = 3

(iii) \(5000 = 2^3 \times 5^4\) → divide by 5
Answer = 5

(iv) \(8192 = 2^{13}\) → divide by \(2\)
Answer = 2

Q6. Find the cube roots of the following numbers.
(i) 1331    (ii) 1728    (iii) 2197    (iv) 2744
Answer:
Cube root means finding a number whose cube gives the given number.

(i) \(11^3 = 1331\) → ∛1331 = 11
(ii) \(12^3 = 1728\) → ∛1728 = 12
(iii) \(13^3 = 2197\) → ∛2197 = 13
(iv) \(14^3 = 2744\) → ∛2744 = 14

(a) The digit in the unit place in the cube of 23 is —

(i) 6
(ii) 7
(iii) 8
(iv) 9

Answer: (ii) 7

(b) Which of the following is a perfect cube?

(i) 652
(ii) 933
(iii) 343
(iv) 1002

Answer: (iii) 343

(c) The value of \( \sqrt[3]{1000} \) is —

(i) 30
(ii) 100
(iii) 10
(iv) 1000

Answer: (iii) 10

(d) If m is the cube root of n then the value of n is —

(i) \( \sqrt{m} \)
(ii) \( \sqrt[3]{m} \)
(iii) \( m^3 \)
(iv) \( m^2 \)

Answer: (iii) \(m^3\)

(e) The value of \( \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} \) is —

(i) 6
(ii) 7
(iii) 8
(iv) 9

Answer: (iv) 9