Square root of 23
√23 = 4.795 to three decimal places; it cannot be simplified.
√23 = 4.795
23 is not a perfect square, so its square root is irrational: a decimal that never ends or repeats. To three decimal places √23 = 4.795; the negative root is −4.795.
23 has no square factor bigger than 1, so √23 cannot be simplified.
Method 1: prime factorisation
23 = 23.
Pair the primes where you can: 1² × 23, so √23 = 1√23.
Method 2: estimate between two squares
4² = 16 and 5² = 25, so √23 is between 4 and 5, closer to 5. One averaging step: (4 + 23/4) ÷ 2 = 4.875, already close to 4.795.
Method 3: the long-division method
| Bring down | Dividend | Divisor | Digit | Remainder |
|---|---|---|---|---|
| 23 | 23 | 4 | 4 | 7 |
| 00 | 700 | 87 | 7 | 91 |
| 00 | 9,100 | 949 | 9 | 559 |
| 00 | 55,900 | 9,585 | 5 | 7,975 |
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: √23 = 4.795 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 √26?
Answer: 5 and 6
3. Simplify √92.
Answer: 2√23
4. Is 24 a perfect square?
Answer: no
5. What is (√23)²?
Answer: 23
📚 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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