Square root of 17
√17 = 4.123 to three decimal places; it cannot be simplified.
√17 = 4.123
17 is not a perfect square, so its square root is irrational: a decimal that never ends or repeats. To three decimal places √17 = 4.123; the negative root is −4.123.
17 has no square factor bigger than 1, so √17 cannot be simplified.
Method 1: prime factorisation
17 = 17.
Pair the primes where you can: 1² × 17, so √17 = 1√17.
Method 2: estimate between two squares
4² = 16 and 5² = 25, so √17 is between 4 and 5, closer to 4. One averaging step: (4 + 17/4) ÷ 2 = 4.125, already close to 4.123.
Method 3: the long-division method
| Bring down | Dividend | Divisor | Digit | Remainder |
|---|---|---|---|---|
| 17 | 17 | 4 | 4 | 1 |
| 00 | 100 | 81 | 1 | 19 |
| 00 | 1,900 | 822 | 2 | 256 |
| 00 | 25,600 | 8,243 | 3 | 871 |
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: √17 = 4.123 to three decimal places.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find √25.
Answer: 5
2. Between which two whole numbers is √20?
Answer: 4 and 5
3. Simplify √68.
Answer: 2√17
4. Is 18 a perfect square?
Answer: no
5. What is (√17)²?
Answer: 17
📚 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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