Math worksheet on using a calculator for powers, roots, and calculations.

Let's solve each part of the problem step by step. These questions are designed to practice using a calculator effectively, especially for powers and roots.

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Question 1: Calculate each of the following

We’ll compute each power:

(a) $ 28^2 $

$$
28^2 = 28 \times 28 = 784
$$

(b) $ 11^3 $

$$
11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331
$$

(c) $ 9^4 $

$$
9^4 = (9^2)^2 = 81^2 = 6561
$$

(d) $ 3^6 $

$$
3^6 = (3^3)^2 = 27^2 = 729
$$

(e) $ 15^8 $

This is large, so we can compute step-by-step or use a calculator:
$$
15^2 = 225 \\
15^4 = (15^2)^2 = 225^2 = 50625 \\
15^8 = (15^4)^2 = 50625^2 = 2,562,890,625
$$

So, $ 15^8 = 2,\!562,\!890,\!625 $

(f) $ 16^0 $

Any non-zero number to the power 0 is 1:
$$
16^0 = 1
$$

(g) $ 2^{13} $

$$
2^{10} = 1024 \\
2^{13} = 2^{10} \times 2^3 = 1024 \times 8 = 8192
$$

(h) $ (-5)^2 $

Negative squared becomes positive:
$$
(-5)^2 = (-5) \times (-5) = 25
$$

(i) $ (-22)^3 $

Odd power of negative number stays negative:
$$
(-22)^3 = - (22^3) = - (22 \times 22 \times 22) = - (484 \times 22) = -10,648
$$

(j) $ (-95)^2 $

Even power → positive:
$$
(-95)^2 = 95^2 = (100 - 5)^2 = 10000 - 2 \times 100 \times 5 + 25 = 10000 - 1000 + 25 = 9025
$$

Or simply: $ 95 \times 95 = 9025 $

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✔ Question 1 Answers:

- (a) 784
- (b) 1331
- (c) 6561
- (d) 729
- (e) 2,562,890,625
- (f) 1
- (g) 8192
- (h) 25
- (i) -10,648
- (j) 9025

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Question 2: Calculate each of the following (roots)

(a) $ \sqrt{576} $

$$
\sqrt{576} = 24 \quad \text{(since } 24^2 = 576)
$$

(b) $ \sqrt{1089} $

$$
\sqrt{1089} = 33 \quad \text{(since } 33^2 = 1089)
$$

(c) $ \sqrt{218089} $

Try estimating:
- $ 460^2 = 211600 $
- $ 470^2 = 220900 $
- Try $ 467^2 = ? $
$$
467^2 = (470 - 3)^2 = 470^2 - 2 \times 470 \times 3 + 9 = 220900 - 2820 + 9 = 218089
$$
So $ \sqrt{218089} = 467 $

(d) $ \sqrt[3]{1000000} $

Note: $ 100^3 = 1,000,000 $, so:
$$
\sqrt[3]{1000000} = 100
$$

(e) $ \sqrt[3]{9261} $

Try cube root:
- $ 20^3 = 8000 $
- $ 21^3 = 21 \times 21 \times 21 = 441 \times 21 = 9261 $
So $ \sqrt[3]{9261} = 21 $

(f) $ \sqrt[4]{81} $

$$
\sqrt[4]{81} = (81)^{1/4} = (3^4)^{1/4} = 3
$$

(g) $ \sqrt[4]{65536} $

Note: $ 2^{16} = 65536 $, so:
$$
\sqrt[4]{65536} = (2^{16})^{1/4} = 2^4 = 16
$$

(h) $ \sqrt[7]{78125} $

Try small numbers:
- $ 5^7 = 5^6 \times 5 = (15625) \times 5 = 78125 $
So $ \sqrt[7]{78125} = 5 $

(i) $ \sqrt[10]{1024} $

Note: $ 2^{10} = 1024 $, so:
$$
\sqrt[10]{1024} = (2^{10})^{1/10} = 2
$$

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✔ Question 2 Answers:

- (a) 24
- (b) 33
- (c) 467
- (d) 100
- (e) 21
- (f) 3
- (g) 16
- (h) 5
- (i) 2

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Question 3: Use your calculator – Give answers to 3 decimal places

(a) $ \sqrt{45} + 3.5^3 $

First, calculate each part:
- $ \sqrt{45} \approx 6.7082 $
- $ 3.5^3 = 3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875 $

Now add:
$$
6.7082 + 42.875 = 49.5832 \approx \boxed{49.583}
$$

(b) $ \sqrt[3]{6} + 1.2^2 $

- $ \sqrt[3]{6} \approx 1.8171 $
- $ 1.2^2 = 1.44 $

Add:
$$
1.8171 + 1.44 = 3.2571 \approx \boxed{3.257}
$$

(c) $ (30.4 - 1.67)^2 $

First subtract:
$$
30.4 - 1.67 = 28.73
$$
Now square:
$$
28.73^2 = 28.73 \times 28.73
$$

Break it down:
$$
(28 + 0.73)^2 = 28^2 + 2 \times 28 \times 0.73 + 0.73^2 = 784 + 40.88 + 0.5329 = 825.4129
$$

So $ \approx \boxed{825.413} $

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✔ Question 3 Answers (to 3 decimal places):

- (a) $ \boxed{49.583} $
- (b) $ \boxed{3.257} $
- (c) $ \boxed{825.413} $

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📌 Summary

All problems involve basic operations with exponents and roots. For Question 3, you're expected to use a calculator and round appropriately.

✔ Final Answers:

#### Question 1:
(a) 784
(b) 1331
(c) 6561
(d) 729
(e) 2,562,890,625
(f) 1
(g) 8192
(h) 25
(i) -10,648
(j) 9025

#### Question 2:
(a) 24
(b) 33
(c) 467
(d) 100
(e) 21
(f) 3
(g) 16
(h) 5
(i) 2

#### Question 3:
(a) 49.583
(b) 3.257
(c) 825.413

Let me know if you'd like a video explanation or how to input these into a calculator!