Use Square and Cube Roots - 8th Grade Math
Card 1 of 25
What is $\sqrt{9}$?
What is $\sqrt{9}$?
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$3$. Since $3^2 = 9$.
$3$. Since $3^2 = 9$.
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What is $\sqrt{4}$?
What is $\sqrt{4}$?
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$2$. Since $2^2 = 4$.
$2$. Since $2^2 = 4$.
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What does the symbol $\sqrt{p}$ represent when $p$ is a positive rational number?
What does the symbol $\sqrt{p}$ represent when $p$ is a positive rational number?
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$\sqrt{p}$ is the positive number whose square is $p$. The square root gives the positive value that when squared equals $p$.
$\sqrt{p}$ is the positive number whose square is $p$. The square root gives the positive value that when squared equals $p$.
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What is the value of $\sqrt{81}$?
What is the value of $\sqrt{81}$?
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$9$. Since $9^2 = 81$.
$9$. Since $9^2 = 81$.
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What is the value of $\sqrt{100}$?
What is the value of $\sqrt{100}$?
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$10$. Since $10^2 = 100$.
$10$. Since $10^2 = 100$.
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What is the value of $\sqrt[3]{1}$?
What is the value of $\sqrt[3]{1}$?
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$1$. Since $1^3 = 1$.
$1$. Since $1^3 = 1$.
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What is the value of $\sqrt[3]{8}$?
What is the value of $\sqrt[3]{8}$?
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$2$. Since $2^3 = 8$.
$2$. Since $2^3 = 8$.
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What is the value of $\sqrt[3]{27}$?
What is the value of $\sqrt[3]{27}$?
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$3$. Since $3^3 = 27$.
$3$. Since $3^3 = 27$.
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What is the value of $\sqrt[3]{64}$?
What is the value of $\sqrt[3]{64}$?
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$4$. Since $4^3 = 64$.
$4$. Since $4^3 = 64$.
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What is the value of $\sqrt[3]{125}$?
What is the value of $\sqrt[3]{125}$?
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$5$. Since $5^3 = 125$.
$5$. Since $5^3 = 125$.
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Which statement is true about $\sqrt{2}$: rational or irrational?
Which statement is true about $\sqrt{2}$: rational or irrational?
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$\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.
$\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.
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What is the value of $\sqrt{1}$?
What is the value of $\sqrt{1}$?
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$1$. Since $1^2 = 1$.
$1$. Since $1^2 = 1$.
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What is the value of $\sqrt{49}$?
What is the value of $\sqrt{49}$?
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$7$. Since $7^2 = 49$.
$7$. Since $7^2 = 49$.
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What is the value of $\sqrt{36}$?
What is the value of $\sqrt{36}$?
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$6$. Since $6^2 = 36$.
$6$. Since $6^2 = 36$.
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What is the value of $\sqrt{25}$?
What is the value of $\sqrt{25}$?
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$5$. Since $5^2 = 25$.
$5$. Since $5^2 = 25$.
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What is the value of $\sqrt{16}$?
What is the value of $\sqrt{16}$?
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$4$. Since $4^2 = 16$.
$4$. Since $4^2 = 16$.
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What is the solution to $x^3=p$ for a positive rational $p$ written using radicals?
What is the solution to $x^3=p$ for a positive rational $p$ written using radicals?
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$x=\sqrt[3]{p}$. Only one real solution exists since cube functions are one-to-one.
$x=\sqrt[3]{p}$. Only one real solution exists since cube functions are one-to-one.
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What are the solutions to $x^2=p$ for a positive rational $p$ written using radicals?
What are the solutions to $x^2=p$ for a positive rational $p$ written using radicals?
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$x=\pm\sqrt{p}$. Both positive and negative roots satisfy the equation since $(\pm\sqrt{p})^2 = p$.
$x=\pm\sqrt{p}$. Both positive and negative roots satisfy the equation since $(\pm\sqrt{p})^2 = p$.
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What does the symbol $\sqrt[3]{p}$ represent when $p$ is a positive rational number?
What does the symbol $\sqrt[3]{p}$ represent when $p$ is a positive rational number?
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$\sqrt[3]{p}$ is the number whose cube is $p$. The cube root gives the value that when cubed equals $p$.
$\sqrt[3]{p}$ is the number whose cube is $p$. The cube root gives the value that when cubed equals $p$.
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What is the value of $\sqrt{9}$?
What is the value of $\sqrt{9}$?
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$3$. Since $3^2 = 9$.
$3$. Since $3^2 = 9$.
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What is the value of $\sqrt{4}$?
What is the value of $\sqrt{4}$?
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$2$. Since $2^2 = 4$.
$2$. Since $2^2 = 4$.
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What is the value of $\sqrt{64}$?
What is the value of $\sqrt{64}$?
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$8$. Since $8^2 = 64$.
$8$. Since $8^2 = 64$.
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What are the solutions to $x^2=p$ when $p>0$ is rational?
What are the solutions to $x^2=p$ when $p>0$ is rational?
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$x=\pm\sqrt{p}$. Square roots have both positive and negative solutions.
$x=\pm\sqrt{p}$. Square roots have both positive and negative solutions.
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What type of number is $\sqrt{2}$?
What type of number is $\sqrt{2}$?
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$\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.
$\sqrt{2}$ is irrational. It cannot be expressed as a ratio of integers.
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What is the solution to $x^3=p$ for a positive rational number $p$?
What is the solution to $x^3=p$ for a positive rational number $p$?
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$x=\sqrt[3]{p}$. Cube roots of positive numbers have only one real solution.
$x=\sqrt[3]{p}$. Cube roots of positive numbers have only one real solution.
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