Use Square and Cube Roots - 8th Grade Math

1. What is the value of $\sqrt[3]{27}$?

   $3$. Since $3^3 = 27$.

2. What is $\sqrt{25}$?

   $5$. Since $5^2 = 25$.

3. What is the value of $\sqrt{100}$?

   $10$. Since $10^2 = 100$.

4. What are the solutions to $x^2=p$ for a positive rational $p$ written using radicals?

   $x=\pm\sqrt{p}$. Both positive and negative roots satisfy the equation since $(\pm\sqrt{p})^2 = p$.

5. What is $\sqrt[3]{125}$?

   $5$. Since $5^3 = 125$.

6. What is the value of $\sqrt{16}$?

   $4$. Since $4^2 = 16$.

7. Which statement is true about $\sqrt{2}$: rational or irrational?

   $\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.

8. What type of number is $\sqrt{2}$?

   $\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.

9. What is the value of $\sqrt[3]{1}$?

   $1$. Since $1^3 = 1$.

10. What is $\sqrt{4}$?

    $2$. Since $2^2 = 4$.

11. What is the value of $\sqrt{25}$?

    $5$. Since $5^2 = 25$.

12. What is $\sqrt{9}$?

    $3$. Since $3^2 = 9$.

13. What is the value of $\sqrt[3]{8}$?

    $2$. Since $2^3 = 8$.

14. What is $\sqrt{100}$?

    $10$. Since $10^2 = 100$.

15. What is the principal square root of $p$ (with $p>0$) written using a radical?

    $\sqrt{p}$. The radical symbol $\sqrt{}$ denotes the non-negative square root.

16. What is the solution to $x^3=p$ for a positive rational number $p$ written with a radical?

    $x=\sqrt[3]{p}$. Cube roots are unique since odd powers preserve sign.

17. What are the solutions to $x^2=p$ for a positive rational number $p$ written with radicals?

    $x=\pm\sqrt{p}$. Since squaring loses sign information, both positive and negative roots work.

18. What does the symbol $\sqrt[3]{p}$ represent when $p$ is a positive rational number?

    $\sqrt[3]{p}$ is the number whose cube is $p$. The cube root gives the value that when cubed equals $p$.

19. What symbol represents the principal (nonnegative) square root of a number $p$?

    The symbol is $\sqrt{p}$. The radical sign denotes the principal (nonnegative) square root.

20. Solve $x^2=49$ and write all solutions.

    $x=\pm 7$. Both $7^2 = 49$ and $(-7)^2 = 49$.

21. What does the symbol $\sqrt{p}$ represent when $p$ is a positive rational number?

    $\sqrt{p}$ is the positive number whose square is $p$. The square root gives the positive value that when squared equals $p$.

22. What is the value of $\sqrt{36}$?

    $6$. Since $6^2 = 36$.

23. What is $\sqrt[3]{8}$?

    $2$. Since $2^3 = 8$.

24. What is the solution to $x^3=p$ for a positive rational number $p$?

    $x=\sqrt[3]{p}$. Cube roots of positive numbers have only one real solution.

25. What is the value of $\sqrt[3]{125}$?

    $5$. Since $5^3 = 125$.

26. What is $\sqrt{49}$?

    $7$. Since $7^2 = 49$.

27. What is $\sqrt{16}$?

    $4$. Since $4^2 = 16$.

28. What is the solution to $x^3=p$ for a positive rational $p$ written using radicals?

    $x=\sqrt[3]{p}$. Only one real solution exists since cube functions are one-to-one.

29. What is $\sqrt[3]{27}$?

    $3$. Since $3^3 = 27$.

30. What is the correct classification of $\sqrt{2}$: rational or irrational?

    $\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.

31. What is $\sqrt[3]{64}$?

    $4$. Since $4^3 = 64$.

32. What is the value of $\sqrt{9}$?

    $3$. Since $3^2 = 9$.

33. What is the value of $\sqrt{1}$?

    $1$. Since $1^2 = 1$.

34. What is $\sqrt[3]{1}$?

    $1$. Since $1^3 = 1$.

35. What is $\sqrt{1}$?

    $1$. Since $1^2 = 1$.

36. What is $\sqrt{81}$?

    $9$. Since $9^2 = 81$.

37. What is the value of $\sqrt{4}$?

    $2$. Since $2^2 = 4$.

38. What is the value of $\sqrt{64}$?

    $8$. Since $8^2 = 64$.

39. What is the value of $\sqrt{81}$?

    $9$. Since $9^2 = 81$.

40. What is the value of $\sqrt[3]{64}$?

    $4$. Since $4^3 = 64$.

41. What is $\sqrt{36}$?

    $6$. Since $6^2 = 36$.

42. What are the solutions to $x^2=p$ when $p>0$ is rational?

    $x=\pm\sqrt{p}$. Square roots have both positive and negative solutions.

43. What is the value of $\sqrt{49}$?

    $7$. Since $7^2 = 49$.

44. What symbol represents the real cube root of a number $p$?

    The symbol is $\sqrt[3]{p}$. The index 3 in the radical indicates the cube root.

45. What is $\sqrt{64}$?

    $8$. Since $8^2 = 64$.

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