Square root of 8
√8 = 2.828 to three decimal places; in simplified form 2√2.
√8 = 2.828
8 is not a perfect square, so its square root is irrational: a decimal that never ends or repeats. To three decimal places √8 = 2.828; the negative root is −2.828.
Simplified radical form: √8 = √(2² × 2) = 2√2.
Method 1: prime factorisation
8 = 23.
Pair the primes where you can: 2² × 2, so √8 = 2√2 = 2.828.
Method 2: estimate between two squares
2² = 4 and 3² = 9, so √8 is between 2 and 3, closer to 3. One averaging step: (2 + 8/2) ÷ 2 = 3.0, already close to 2.828.
Method 3: the long-division method
| Bring down | Dividend | Divisor | Digit | Remainder |
|---|---|---|---|---|
| 08 | 8 | 2 | 2 | 4 |
| 00 | 400 | 48 | 8 | 16 |
| 00 | 1,600 | 562 | 2 | 476 |
| 00 | 47,600 | 5,648 | 8 | 2,416 |
Pair the digits from the decimal point; each digit of the root is the largest d with (20 × root so far + d) × d ≤ the dividend. Result: √8 = 2.828 to three decimal places.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find √9.
Answer: 3
2. Between which two whole numbers is √11?
Answer: 3 and 4
3. Simplify √32.
Answer: 4√2
4. Is 9 a perfect square?
Answer: yes
5. What is (√8)²?
Answer: 8
📚 The class this belongs to
Square roots are taught in Grade 8 in the US (Common Core 8.EE.2), Year 7 and 8 in the UK, Class 8 in CBSE (NCERT Class 8, Squares and Square Roots) and Year 8 in Australia.
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