8th Grade Math Flashcards: Use Square And Cube Roots

What this deck covers

This deck focuses on Use Square And Cube Roots, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is $\sqrt{9}$?

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

Flashcard 2: What is $\sqrt{4}$?

Answer: $2$. Since $2^2 = 4$.

Flashcard 3: What does the symbol $\sqrt{p}$ represent when $p$ is a positive rational number?

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

Flashcard 4: What is the value of $\sqrt{81}$?

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

Flashcard 5: What is the value of $\sqrt{100}$?

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

Flashcard 6: What is the value of $\sqrt[3]{1}$?

Answer: $1$. Since $1^3 = 1$.

Flashcard 7: What is the value of $\sqrt[3]{8}$?

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

Flashcard 8: What is the value of $\sqrt[3]{27}$?

Answer: $3$. Since $3^3 = 27$.

Flashcard 9: What is the value of $\sqrt[3]{64}$?

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

Flashcard 10: What is the value of $\sqrt[3]{125}$?

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

Flashcard 11: Which statement is true about $\sqrt{2}$: rational or irrational?

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

Flashcard 12: What is the value of $\sqrt{1}$?

Answer: $1$. Since $1^2 = 1$.

Flashcard 13: What is the value of $\sqrt{49}$?

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

Flashcard 14: What is the value of $\sqrt{36}$?

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

Flashcard 15: What is the value of $\sqrt{25}$?

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

Flashcard 16: What is the value of $\sqrt{16}$?

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

Flashcard 17: What is the solution to $x^3=p$ for a positive rational $p$ written using radicals?

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

Flashcard 18: What are the solutions to $x^2=p$ for a positive rational $p$ written using radicals?

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

Flashcard 19: What does the symbol $\sqrt[3]{p}$ represent when $p$ is a positive rational number?

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

Flashcard 20: What is the value of $\sqrt{9}$?

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

Flashcard 21: What is the value of $\sqrt{4}$?

Answer: $2$. Since $2^2 = 4$.

Flashcard 22: What is the value of $\sqrt{64}$?

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

Flashcard 23: What are the solutions to $x^2=p$ when $p>0$ is rational?

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

Flashcard 24: What type of number is $\sqrt{2}$?

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

Flashcard 25: What is the solution to $x^3=p$ for a positive rational number $p$?

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

Flashcard 26: What symbol represents the real cube root of a number $p$?

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

Flashcard 27: What symbol represents the principal (nonnegative) square root of a number $p$?

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

Flashcard 28: What is $\sqrt{100}$?

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

Flashcard 29: What is the correct classification of $\sqrt{2}$: rational or irrational?

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

Flashcard 30: Solve $x^2=49$ and write all solutions.

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