Practice simplifying and calculating expressions with this adding and subtracting 3 square roots worksheet.

To solve the problems involving adding and subtracting square roots, we need to simplify each square root first and then perform the required arithmetic operations. Let's go through each problem step by step.

Problem 1: \( \sqrt{400} + \sqrt{144} + \sqrt{16} \)

- Simplify each square root:
- \( \sqrt{400} = 20 \)
- \( \sqrt{144} = 12 \)
- \( \sqrt{16} = 4 \)
- Add them together:
\[
20 + 12 + 4 = 36
\]
- Answer: \( 36 \)

Problem 2: \( \sqrt{49} - \sqrt{121} - \sqrt{16} \)

- Simplify each square root:
- \( \sqrt{49} = 7 \)
- \( \sqrt{121} = 11 \)
- \( \sqrt{16} = 4 \)
- Perform the subtraction:
\[
7 - 11 - 4 = -8
\]
- Answer: \( -8 \)

Problem 3: \( \sqrt{25} + \sqrt{1} + \sqrt{441} \)

- Simplify each square root:
- \( \sqrt{25} = 5 \)
- \( \sqrt{1} = 1 \)
- \( \sqrt{441} = 21 \)
- Add them together:
\[
5 + 1 + 21 = 27
\]
- Answer: \( 27 \)

Problem 4: \( \sqrt{0} - \sqrt{36} - \sqrt{225} \)

- Simplify each square root:
- \( \sqrt{0} = 0 \)
- \( \sqrt{36} = 6 \)
- \( \sqrt{225} = 15 \)
- Perform the subtraction:
\[
0 - 6 - 15 = -21
\]
- Answer: \( -21 \)

Problem 5: \( \sqrt{49} + \sqrt{400} + \sqrt{25} \)

- Simplify each square root:
- \( \sqrt{49} = 7 \)
- \( \sqrt{400} = 20 \)
- \( \sqrt{25} = 5 \)
- Add them together:
\[
7 + 20 + 5 = 32
\]
- Answer: \( 32 \)

Problem 6: \( \sqrt{900} - \sqrt{81} - \sqrt{4} \)

- Simplify each square root:
- \( \sqrt{900} = 30 \)
- \( \sqrt{81} = 9 \)
- \( \sqrt{4} = 2 \)
- Perform the subtraction:
\[
30 - 9 - 2 = 19
\]
- Answer: \( 19 \)

Problem 7: \( \sqrt{225} + \sqrt{25} + \sqrt{25} \)

- Simplify each square root:
- \( \sqrt{225} = 15 \)
- \( \sqrt{25} = 5 \)
- \( \sqrt{25} = 5 \)
- Add them together:
\[
15 + 5 + 5 = 25
\]
- Answer: \( 25 \)

Problem 8: \( \sqrt{49} - \sqrt{400} - \sqrt{100} \)

- Simplify each square root:
- \( \sqrt{49} = 7 \)
- \( \sqrt{400} = 20 \)
- \( \sqrt{100} = 10 \)
- Perform the subtraction:
\[
7 - 20 - 10 = -23
\]
- Answer: \( -23 \)

Problem 9: \( \sqrt{400} - \sqrt{121} - \sqrt{144} \)

- Simplify each square root:
- \( \sqrt{400} = 20 \)
- \( \sqrt{121} = 11 \)
- \( \sqrt{144} = 12 \)
- Perform the subtraction:
\[
20 - 11 - 12 = -3
\]
- Answer: \( -3 \)

Problem 10: \( \sqrt{64} + \sqrt{9} + \sqrt{0} \)

- Simplify each square root:
- \( \sqrt{64} = 8 \)
- \( \sqrt{9} = 3 \)
- \( \sqrt{0} = 0 \)
- Add them together:
\[
8 + 3 + 0 = 11
\]
- Answer: \( 11 \)

Problem 11: \( \sqrt{289} - \sqrt{4} - \sqrt{1} \)

- Simplify each square root:
- \( \sqrt{289} = 17 \)
- \( \sqrt{4} = 2 \)
- \( \sqrt{1} = 1 \)
- Perform the subtraction:
\[
17 - 2 - 1 = 14
\]
- Answer: \( 14 \)

Problem 12: \( \sqrt{9} + \sqrt{81} + \sqrt{25} \)

- Simplify each square root:
- \( \sqrt{9} = 3 \)
- \( \sqrt{81} = 9 \)
- \( \sqrt{25} = 5 \)
- Add them together:
\[
3 + 9 + 5 = 17
\]
- Answer: \( 17 \)

Problem 13: \( \sqrt{196} + \sqrt{529} + \sqrt{36} \)

- Simplify each square root:
- \( \sqrt{196} = 14 \)
- \( \sqrt{529} = 23 \)
- \( \sqrt{36} = 6 \)
- Add them together:
\[
14 + 23 + 6 = 43
\]
- Answer: \( 43 \)

Problem 14: \( \sqrt{121} - \sqrt{25} - \sqrt{400} \)

- Simplify each square root:
- \( \sqrt{121} = 11 \)
- \( \sqrt{25} = 5 \)
- \( \sqrt{400} = 20 \)
- Perform the subtraction:
\[
11 - 5 - 20 = -14
\]
- Answer: \( -14 \)

Problem 15: \( \sqrt{1} + \sqrt{25} + \sqrt{36} \)

- Simplify each square root:
- \( \sqrt{1} = 1 \)
- \( \sqrt{25} = 5 \)
- \( \sqrt{36} = 6 \)
- Add them together:
\[
1 + 5 + 6 = 12
\]
- Answer: \( 12 \)

Problem 16: \( \sqrt{4} - \sqrt{25} - \sqrt{324} \)

- Simplify each square root:
- \( \sqrt{4} = 2 \)
- \( \sqrt{25} = 5 \)
- \( \sqrt{324} = 18 \)
- Perform the subtraction:
\[
2 - 5 - 18 = -21
\]
- Answer: \( -21 \)

Problem 17: \( \sqrt{49} + \sqrt{121} + \sqrt{64} \)

- Simplify each square root:
- \( \sqrt{49} = 7 \)
- \( \sqrt{121} = 11 \)
- \( \sqrt{64} = 8 \)
- Add them together:
\[
7 + 11 + 8 = 26
\]
- Answer: \( 26 \)

Problem 18: \( \sqrt{25} - \sqrt{49} - \sqrt{49} \)

- Simplify each square root:
- \( \sqrt{25} = 5 \)
- \( \sqrt{49} = 7 \)
- \( \sqrt{49} = 7 \)
- Perform the subtraction:
\[
5 - 7 - 7 = -9
\]
- Answer: \( -9 \)

Problem 19: \( \sqrt{841} + \sqrt{144} + \sqrt{9} \)

- Simplify each square root:
- \( \sqrt{841} = 29 \)
- \( \sqrt{144} = 12 \)
- \( \sqrt{9} = 3 \)
- Add them together:
\[
29 + 12 + 3 = 44
\]
- Answer: \( 44 \)

Problem 20: \( \sqrt{81} - \sqrt{25} - \sqrt{256} \)

- Simplify each square root:
- \( \sqrt{81} = 9 \)
- \( \sqrt{25} = 5 \)
- \( \sqrt{256} = 16 \)
- Perform the subtraction:
\[
9 - 5 - 16 = -12
\]
- Answer: \( -12 \)

Problem 21: \( \sqrt{400} - \sqrt{36} - \sqrt{625} \)

- Simplify each square root:
- \( \sqrt{400} = 20 \)
- \( \sqrt{36} = 6 \)
- \( \sqrt{625} = 25 \)
- Perform the subtraction:
\[
20 - 6 - 25 = -11
\]
- Answer: \( -11 \)

Problem 22: \( \sqrt{25} + \sqrt{9} + \sqrt{1} \)

- Simplify each square root:
- \( \sqrt{25} = 5 \)
- \( \sqrt{9} = 3 \)
- \( \sqrt{1} = 1 \)
- Add them together:
\[
5 + 3 + 1 = 9
\]
- Answer: \( 9 \)

Problem 23: \( \sqrt{400} - \sqrt{16} - \sqrt{4} \)

- Simplify each square root:
- \( \sqrt{400} = 20 \)
- \( \sqrt{16} = 4 \)
- \( \sqrt{4} = 2 \)
- Perform the subtraction:
\[
20 - 4 - 2 = 14
\]
- Answer: \( 14 \)

Problem 24: \( \sqrt{1} + \sqrt{36} + \sqrt{64} \)

- Simplify each square root:
- \( \sqrt{1} = 1 \)
- \( \sqrt{36} = 6 \)
- \( \sqrt{64} = 8 \)
- Add them together:
\[
1 + 6 + 8 = 15
\]
- Answer: \( 15 \)

Final Answer:

\[
\boxed{
\begin{array}{ll}
36 & 43 \\
-8 & -14 \\
27 & 12 \\
-21 & -21 \\
32 & 26 \\
19 & -9 \\
25 & 44 \\
-23 & -12 \\
-3 & -11 \\
11 & 9 \\
14 & 14 \\
17 & 15 \\
\end{array}
}
\]