Cube Roots worksheet - Free Printable

Let's solve each cube root step by step. The cube root of a number is the value that, when multiplied by itself three times, gives the original number.

We are asked to find:

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1. $ \sqrt[3]{729} $

We look for a number such that $ x^3 = 729 $.
Try:
$ 9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729 $ ✔
So, $ \sqrt[3]{729} = 9 $

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2. $ \sqrt[3]{1000} $

$ 10^3 = 10 \times 10 \times 10 = 1000 $ ✔
So, $ \sqrt[3]{1000} = 10 $

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3. $ \sqrt[3]{1} $

$ 1^3 = 1 $ ✔
So, $ \sqrt[3]{1} = 1 $

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4. $ \sqrt[3]{2197} $

Try $ 13^3 $:
$ 13 \times 13 = 169 $, then $ 169 \times 13 = 2197 $ ✔
So, $ \sqrt[3]{2197} = 13 $

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5. $ \sqrt[3]{64} $

$ 4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64 $ ✔
So, $ \sqrt[3]{64} = 4 $

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6. $ \sqrt[3]{27} $

$ 3^3 = 3 \times 3 \times 3 = 27 $ ✔
So, $ \sqrt[3]{27} = 3 $

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7. $ \sqrt[3]{512} $

$ 8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512 $ ✔
So, $ \sqrt[3]{512} = 8 $

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8. $ \sqrt[3]{216} $

$ 6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216 $ ✔
So, $ \sqrt[3]{216} = 6 $

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9. $ \sqrt[3]{125} $

$ 5^3 = 5 \times 5 \times 5 = 25 \times 5 = 125 $ ✔
So, $ \sqrt[3]{125} = 5 $

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10. $ \sqrt[3]{343} $

Try $ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 $ ✔
So, $ \sqrt[3]{343} = 7 $

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✔ Final Answers:

$$
\begin{align*}
\sqrt[3]{729} &= 9 \\
\sqrt[3]{1000} &= 10 \\
\sqrt[3]{1} &= 1 \\
\sqrt[3]{2197} &= 13 \\
\sqrt[3]{64} &= 4 \\
\sqrt[3]{27} &= 3 \\
\sqrt[3]{512} &= 8 \\
\sqrt[3]{216} &= 6 \\
\sqrt[3]{125} &= 5 \\
\sqrt[3]{343} &= 7 \\
\end{align*}
$$

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✔ Tip: Memorizing small cubes helps:
- $ 1^3 = 1 $
- $ 2^3 = 8 $
- $ 3^3 = 27 $
- $ 4^3 = 64 $
- $ 5^3 = 125 $
- $ 6^3 = 216 $
- $ 7^3 = 343 $
- $ 8^3 = 512 $
- $ 9^3 = 729 $
- $ 10^3 = 1000 $
- $ 13^3 = 2197 $

This makes cube roots much faster!