Square and Cube Root of a number. worksheet - Free Printable

Let's solve each part of the problem step by step.

---

A. Find the answer, show your working

We are dealing with exponents (powers).

#### 1) $ 2^2 = 2 \times 2 = 4 $ ✔ (Given)

#### 2) $ 2^4 = 2 \times 2 \times 2 \times 2 = 16 $

#### 3) $ 3^2 = 3 \times 3 = 9 $

#### 4) $ 4^3 = 4 \times 4 \times 4 = 64 $

#### 5) $ 5^2 = 5 \times 5 = 25 $

#### 6) $ 10^3 = 10 \times 10 \times 10 = 1000 $

#### 7) $ 12^2 = 12 \times 12 = 144 $

#### 8) $ 8^3 = 8 \times 8 \times 8 = 512 $

#### 9) $ 7^2 = 7 \times 7 = 49 $

#### 10) $ 4^3 = 4 \times 4 \times 4 = 64 $

---

B. Find the answer

These are square roots (denoted by $ \sqrt{} $ or $ ^2\sqrt{} $).

> Note: $ \sqrt{x} $ means the positive square root of $ x $.

#### 11) $ \sqrt{16} = 4 $ ✔ (Given)

#### 12) $ \sqrt{25} = 5 $ because $ 5 \times 5 = 25 $

#### 13) $ \sqrt{100} = 10 $ because $ 10 \times 10 = 100 $

#### 14) $ \sqrt{81} = 9 $ because $ 9 \times 9 = 81 $

#### 15) $ \sqrt{144} = 12 $ because $ 12 \times 12 = 144 $

#### 16) $ \sqrt{1600} = 40 $ because $ 40 \times 40 = 1600 $

#### 17) $ \sqrt{8100} = 90 $ because $ 90 \times 90 = 8100 $

#### 18) $ \sqrt{49} = 7 $ because $ 7 \times 7 = 49 $

#### 19) $ \sqrt{121} = 11 $ because $ 11 \times 11 = 121 $

#### 20) $ \sqrt{64} = 8 $ because $ 8 \times 8 = 64 $

---

C. Find the answer

These are cube roots, denoted by $ \sqrt[3]{} $ or $ ^3\sqrt{} $.

> Cube root of $ x $ is a number that, when multiplied by itself three times, gives $ x $.

#### 21) $ \sqrt[3]{8} = 2 $ because $ 2 \times 2 \times 2 = 8 $

#### 22) $ \sqrt[3]{27} = 3 $ because $ 3 \times 3 \times 3 = 27 $

#### 23) $ \sqrt[3]{125} = 5 $ because $ 5 \times 5 \times 5 = 125 $

#### 24) $ \sqrt[3]{1000} = 10 $ because $ 10 \times 10 \times 10 = 1000 $

#### 25) $ \sqrt[3]{512} = 8 $ because $ 8 \times 8 \times 8 = 512 $

#### 26) $ \sqrt[3]{125} = 5 $ (same as #23)

#### 27) $ \sqrt[3]{64} = 4 $ because $ 4 \times 4 \times 4 = 64 $

#### 28) $ \sqrt[3]{343} = 7 $ because $ 7 \times 7 \times 7 = 343 $

#### 29) $ \sqrt[3]{729} = 9 $ because $ 9 \times 9 \times 9 = 729 $

#### 30) $ \sqrt[3]{216} = 6 $ because $ 6 \times 6 \times 6 = 216 $

---

✔ Final Answers:

#### A.
1) 4
2) 16
3) 9
4) 64
5) 25
6) 1000
7) 144
8) 512
9) 49
10) 64

#### B.
11) 4
12) 5
13) 10
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) 8

#### C.
21) 2
22) 3
23) 5
24) 10
25) 8
26) 5
27) 4
28) 7
29) 9
30) 6

---

Let me know if you'd like these explained in a different format (e.g., for a student learning powers and roots).