√16 at a glance
- Exact value
- 4
- Decimal (10 places)
- 4
- Rounded
- 4
- Perfect square?
- Yes — 4²
- Rational?
- Rational (whole number)
- Both square roots
- ±4
- Prime factorization
- 2⁴
- Cube root
- 2.519842
How to simplify √16
Write 16 as a product of primes and halve every exponent. Because each exponent is even, nothing is left under the radical sign:
√16 = 2² = 4
16 has 3 factor pairs (1 × 16, 2 × 8, 4 × 4). The pair with two equal numbers, 4 × 4, 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 16 = 1 + 3 + 5 + 7, the first 4 odd numbers.
Where √16 sits between perfect squares
16 is 4². The perfect squares on either side are 9 (3²) and 25 (5²), so the gaps are 7 below and 9 above — consecutive squares always differ by consecutive odd numbers.
Finding √16 with the Babylonian method
Picture a rectangle with an area of 16 and one side x; the other side must be 16 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √16.
To show the method at work on a perfect square, start one above the answer, at 5:
| Step | Guess x | 16 ÷ x | Average | Correct decimals |
|---|---|---|---|---|
| 1 | 5.0000000000 | 3.2000000000 | 4.1000000000 | 1 |
| 2 | 4.1000000000 | 3.9024390244 | 4.0012195122 | 2 |
| 3 | 4.0012195122 | 3.9987808595 | 4.0000001858 | 6 |
| 4 | 4.0000001858 | 3.9999998142 | 4.0000000000 | all 10 shown |
The count of correct decimals went 1, 2, 6 and all 10 over 4 steps — roughly doubling each time — until the guess matched √16 = 4.0000000000 to every decimal shown.
√16 in geometry and everyday measurements
- A square tile with an area of 16 square inches has sides exactly 4 in long.
- 16 is not a sum of two whole-number squares — no pair of squares adds up to it — so √16 is never the diagonal of a rectangle with whole-number sides. It is not a sum of three positive squares either, so no whole-number box has √16 as its space diagonal.
Square roots near √16 and related roots
| Root | Simplest form | Decimal | Perfect square? |
|---|---|---|---|
| √13 | √13 | 3.6056 | No |
| √14 | √14 | 3.7417 | No |
| √15 | √15 | 3.8730 | No |
| √16 | 4 | 4.0000 | Yes |
| √17 | √17 | 4.1231 | No |
| √18 | 3√2 | 4.2426 | No |
| √19 | √19 | 4.3589 | No |
- The cube root of 16 is about 2.519842.
- Taking the square root twice gives the fourth root: √4 = 2, so 16 = 2⁴.
- Four times the radicand doubles the root: √64 = 2 × √16 ≈ 8.
Frequently asked questions
What is the square root of 16?
The square root of 16 is 4, because 4 × 4 = 16. Strictly, 16 has two square roots, 4 and −4; the √ symbol means the positive one.
Is the square root of 16 rational or irrational?
Rational. 16 is a perfect square, so its square root is the whole number 4.
Can √16 be simplified?
Yes, all the way to a whole number: √16 = 4.
What is √16 rounded to two decimal places?
√16 is exactly 4, or 4.00 written to two decimal places.