√676 at a glance
- Exact value
- 26
- Decimal (10 places)
- 26
- Rounded
- 26
- Perfect square?
- Yes — 26²
- Rational?
- Rational (whole number)
- Both square roots
- ±26
- Prime factorization
- 2² × 13²
- Cube root
- 8.776383
How to simplify √676
Write 676 as a product of primes and halve every exponent. Because each exponent is even, nothing is left under the radical sign:
√676 = 2 × 13 = 26
676 has 5 factor pairs (1 × 676, 2 × 338, 4 × 169, 13 × 52, 26 × 26). The pair with two equal numbers, 26 × 26, is what makes it a perfect square — and why it has an odd number of factors.
Every perfect square is also a sum of consecutive odd numbers starting at 1. Here 676 = 1 + 3 + 5 + 7 + … + 51, the first 26 odd numbers.
Where √676 sits between perfect squares
676 is 26². The perfect squares on either side are 625 (25²) and 729 (27²), so the gaps are 51 below and 53 above — consecutive squares always differ by consecutive odd numbers.
Finding √676 with the Babylonian method
Picture a rectangle with an area of 676 and one side x; the other side must be 676 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √676.
To show the method at work on a perfect square, start one above the answer, at 27:
| Step | Guess x | 676 ÷ x | Average | Correct decimals |
|---|---|---|---|---|
| 1 | 27.0000000000 | 25.0370370370 | 26.0185185185 | 1 |
| 2 | 26.0185185185 | 25.9814946619 | 26.0000065902 | 5 |
| 3 | 26.0000065902 | 25.9999934098 | 26.0000000000 | all 10 shown |
The count of correct decimals went 1, 5 and all 10 over 3 steps — roughly doubling each time — until the guess matched √676 = 26.0000000000 to every decimal shown.
√676 in geometry and everyday measurements
- 676 square feet is 62.8 m². Laid out as a square — a small house footprint or a lot — it is exactly 26 ft (26 ft) on a side.
- 676 = 10² + 24², so 10, 24 and 26 form a Pythagorean triple: a right triangle with legs 10 and 24 has a hypotenuse of exactly 26.
Square roots near √676 and related roots
| Root | Simplest form | Decimal | Perfect square? |
|---|---|---|---|
| √673 | √673 | 25.9422 | No |
| √674 | √674 | 25.9615 | No |
| √675 | 15√3 | 25.9808 | No |
| √676 | 26 | 26.0000 | Yes |
| √677 | √677 | 26.0192 | No |
| √678 | √678 | 26.0384 | No |
| √679 | √679 | 26.0576 | No |
- The cube root of 676 is about 8.776383.
- Taking the square root twice gives the fourth root: √26 ≈ 5.099020.
- Because 676 = 4 × 169, the root is twice √169: 2 × 13 ≈ 26.
Frequently asked questions
What is the square root of 676?
The square root of 676 is 26, because 26 × 26 = 676. Strictly, 676 has two square roots, 26 and −26; the √ symbol means the positive one.
Is the square root of 676 rational or irrational?
Rational. 676 is a perfect square, so its square root is the whole number 26.
Can √676 be simplified?
Yes, all the way to a whole number: √676 = 26.
What is √676 rounded to two decimal places?
√676 is exactly 26, or 26.00 written to two decimal places.