Free square root worksheets (PDF and html) - Free Printable

Here's the step-by-step solution to each problem on the Square Roots Worksheet, with answers rounded to 3 decimal places as instructed.

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1 a.  √(2 × 83.5)

Step 1: Multiply inside the square root:
2 × 83.5 = 167

Step 2: Take the square root:
√167 ≈ 12.922847...

Step 3: Round to 3 decimals:
→ 12.923

✔ Answer: 12.923

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1 b.  (√8)²

Step 1: Remember that (√a)² = a, for any non-negative number *a*.
So, (√8)² = 8

✔ Answer: 8.000

*(Note: Even though it’s an integer, we write it with 3 decimal places as requested.)*

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2 a.  √20 − √181

Step 1: Calculate √20 ≈ 4.472135...

Step 2: Calculate √181 ≈ 13.453624...

Step 3: Subtract:
4.472135 - 13.453624 ≈ -8.981489

Step 4: Round to 3 decimals:
→ -8.981

✔ Answer: -8.981

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2 b.  √(2 + 28)

Step 1: Add inside the square root:
2 + 28 = 30

Step 2: Take the square root:
√30 ≈ 5.477225...

Step 3: Round to 3 decimals:
→ 5.477

✔ Answer: 5.477

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3 a.  √223 / √35

Step 1: Use the property: √a / √b = √(a/b)
So, √223 / √35 = √(223/35)

Step 2: Compute 223 ÷ 35 ≈ 6.371428...

Step 3: Take the square root:
√6.371428 ≈ 2.524168...

Step 4: Round to 3 decimals:
→ 2.524

✔ Answer: 2.524

*(Alternatively, you could compute √223 ≈ 14.933 and √35 ≈ 5.916, then divide: 14.933 / 5.916 ≈ 2.524 — same result.)*

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3 b.  (√56)²

Step 1: Again, (√a)² = a
So, (√56)² = 56

✔ Answer: 56.000

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4 a.  √(494 − 271)

Step 1: Subtract inside the square root:
494 − 271 = 223

Step 2: Take the square root:
√223 ≈ 14.933184...

Step 3: Round to 3 decimals:
→ 14.933

✔ Answer: 14.933

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4 b.  √(470 / 5)

Step 1: Divide inside the square root:
470 ÷ 5 = 94

Step 2: Take the square root:
√94 ≈ 9.695359...

Step 3: Round to 3 decimals:
→ 9.695

✔ Answer: 9.695

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5 a.  (√299)²

Step 1: (√a)² = a
So, (√299)² = 299

✔ Answer: 299.000

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5 b.  √(110²)

Step 1: Square first: 110² = 12100

Step 2: Take square root:
√12100 = 110

*(Because √(a²) = |a|, and since 110 is positive, √(110²) = 110)*

✔ Answer: 110.000

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## ✔ Final Answers (Rounded to 3 Decimal Places):

| Problem | Answer |
|---------|------------|
| 1 a. | 12.923 |
| 1 b. | 8.000 |
| 2 a. | -8.981 |
| 2 b. | 5.477 |
| 3 a. | 2.524 |
| 3 b. | 56.000 |
| 4 a. | 14.933 |
| 4 b. | 9.695 |
| 5 a. | 299.000|
| 5 b. | 110.000|

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