Square root of 35
√35 = 5.916 to three decimal places; it cannot be simplified.
√35 = 5.916
35 is not a perfect square, so its square root is irrational: a decimal that never ends or repeats. To three decimal places √35 = 5.916; the negative root is −5.916.
35 has no square factor bigger than 1, so √35 cannot be simplified.
Method 1: prime factorisation
35 = 5 × 7.
Pair the primes where you can: 1² × 35, so √35 = 1√35.
Method 2: estimate between two squares
5² = 25 and 6² = 36, so √35 is between 5 and 6, closer to 6. One averaging step: (5 + 35/5) ÷ 2 = 6.0, already close to 5.916.
Method 3: the long-division method
| Bring down | Dividend | Divisor | Digit | Remainder |
|---|---|---|---|---|
| 35 | 35 | 5 | 5 | 10 |
| 00 | 1,000 | 109 | 9 | 19 |
| 00 | 1,900 | 1,181 | 1 | 719 |
| 00 | 71,900 | 11,826 | 6 | 944 |
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: √35 = 5.916 to three decimal places.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find √36.
Answer: 6
2. Between which two whole numbers is √38?
Answer: 6 and 7
3. Simplify √140.
Answer: 2√35
4. Is 36 a perfect square?
Answer: yes
5. What is (√35)²?
Answer: 35
📚 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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