Exponents, Square & Cube Roots Quiz - ICSE Class 6 Mathematics

Free practice quiz: Exponents, Square & Cube Roots (ICSE Class 6 Mathematics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 6 Mathematics practice quiz has 51 multiple-choice questions on Exponents, Square & Cube Roots, and 51 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If $2^x = 16$, what is the value of $x$? Also, find the value of $x^2$.

   1. x = 4, x^2 = 16
   2. x = 2, x^2 = 4
   3. x = 8, x^2 = 64
   4. x = 16, x^2 = 256
   Show answer

   Answer: A. x = 4, x^2 = 16

   To solve $2^x = 16$, we need to express 16 as a power of 2. Since $2^4 = 16$, we have $x = 4$. Then, $x^2 = 4^2 = 16$.

2. What is the cube root of 125?

   1. 4
   2. 5
   3. 6
   4. 25
   Show answer

   Answer: B. 5

   We are looking for a number that, when multiplied by itself three times, equals 125. Since $5 imes 5 imes 5 = 125$, the cube root of 125 is 5.

3. Calculate the value of $3^4$.

   1. 12
   2. 27
   3. 64
   4. 81
   Show answer

   Answer: D. 81

   $3^4$ means 3 multiplied by itself four times: $3 imes 3 imes 3 imes 3 = 9 imes 9 = 81$.

4. Simplify $\frac{7^8}{7^4}$.

   1. 7^4
   2. 7^32
   3. 7^2
   4. 7^12
   Show answer

   Answer: A. 7^4

   When dividing exponents with the same base, we subtract the powers. So, $\frac{7^8}{7^4} = 7^{8-4} = 7^4$.

5. Evaluate $4^3 - 2^4$.

   1. 48
   2. 32
   3. 16
   4. 64
   Show answer

   Answer: A. 48

   $4^3 = 4 imes 4 imes 4 = 64$. $2^4 = 2 imes 2 imes 2 imes 2 = 16$. So, $64 - 16 = 48$.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Simplify the expression: $(3^2)^3$.
2. Evaluate the expression: $5^3 - \sqrt{100}$.
3. If $3^y = 81$, what is the value of $y$? And what is $y^3$?
4. Which of the following is the cube root of 343?
5. Simplify $2^3 imes 2^4$.
6. What is the value of $\sqrt{25} + \sqrt{81}$?
7. Calculate $10^3$.
8. If $x^2 = 49$, and $x$ is a positive integer, what is the value of $x$?
9. Simplify $\frac{5^7}{5^3}$.
10. Calculate the value of $2^5$.
11. If $4^a = 64$, what is the value of $a$?
12. What is the square root of 100?
13. Simplify $(3^2)^2$.
14. Which of the following numbers is a perfect cube?
15. Evaluate $6^2 + 3^3$.
16. If $x^3 = 27$, what is the value of $x$?
17. What is the value of $7^2$? And what is $\sqrt{49}$?
18. Simplify $4^2 imes 4^3$.
19. Which of the following is the square root of 169?
20. If $5^x = 125$, what is the value of $x$? Also, find the value of $x^2$.
21. Simplify $10^5 imes 10^2$.
22. Calculate the value of $\sqrt{144} + \sqrt{16}$.
23. What is the cube root of 64?
24. Simplify $(2^4)^3$.
25. If $6^y = 216$, what is the value of $y$?
26. Calculate $12^2$.
27. What is the value of $\sqrt{16} imes \sqrt{25}$?
28. If $x^2 = 81$ and $x$ is a positive integer, what is the value of $x$? And what is $x^3$?
29. What is the value of $8^2$? And what is the cube root of 512?
30. Simplify $3^5 imes 3^2$.
31. Calculate the value of $2^6$.
32. Which of the following numbers is a perfect square?
33. If $7^x = 49$, what is the value of $x$?
34. Calculate the value of $\sqrt{121} + \sqrt{100}$.
35. Simplify $(5^3)^2$.
36. What is the cube root of 216?
37. If $x^3 = 125$, what is the value of $x$? And what is $x^2$?
38. Calculate the value of $5^3$.
39. Simplify $8^3 \div 8^2$.
40. What is the square root of 36?
41. If $3^x = 27$, what is the value of $x$? And what is $x^2$?
42. Which of the following is a perfect cube?
43. Simplify $(10^2)^3$.
44. Calculate the value of $\sqrt{49} imes \sqrt{9}$.
45. If $2^x = 32$, what is the value of $x$?
46. What is the value of $9^2$? And what is the square root of 81?

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