Square Root of 944

√944 at a glance

Exact value

4√59

Decimal (10 places)

30.7245829915

Rounded

30.7 · 30.72 · 30.725

Perfect square?

No — between 30² and 31²

Rational?

Irrational

Both square roots

±30.724583

Prime factorization

2⁴ × 59

Cube root

9.809736

How to simplify √944

Look for the largest perfect square that divides 944. Here it is 16 (4²), because 944 = 16 × 59 and 59 has no square factor left:

The prime factorization tells the same story: 944 = 2⁴ × 59. Each pair of equal primes leaves the radical as one factor, so 2² comes out and 59 stays inside.

944 has 2 square factors (4 and 16). Starting with a smaller one still works but takes more rounds: √944 = 2√236, and √236 can be simplified again. Using 16 straight away finishes in one step.

Check: (4√59)² = 4² × 59 = 16 × 59 = 944. As a decimal, 4√59 = 4 × 7.6811457479 ≈ 30.7245829915.

Where √944 sits between perfect squares

900 = 30² and 961 = 31² are the nearest perfect squares, so √944 lies between 30 and 31. 944 is 44 above 900 and 17 below 961, so the root is closer to 31.

• Straight line between 900 and 961: 30.7213 (0.01% low)
• Tangent from 30, i.e. 30 + 44 ÷ 60: 30.7333 (0.03% high)
• Tangent from 31, i.e. 31 − 17 ÷ 62: 30.7258 (0% high)

For √944 the tangent at 31 wins, missing by only 0.0012. Tangent estimates shine when the number sits close to a perfect square — here 944 is just 17 below 961.

Finding √944 with the Babylonian method

Picture a rectangle with an area of 944 and one side x; the other side must be 944 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √944.

Start from the nearest whole number, 31 (31² = 961):

The count of correct decimals went 2, 7 and all 10 over 3 steps — roughly doubling each time — until the guess matched √944 = 30.7245829915 to every decimal shown.

√944 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √944 the pattern is [30; 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 1, 1, …] with the block of 16 terms after the semicolon repeating forever (only the first 12 of the 16 are shown). A pattern that never ends is one more proof that √944 is irrational.

Cutting the continued fraction off early gives the best fractions for approximating the root — no fraction with a smaller denominator comes closer:

The same fractions solve Pell’s equation, x² − 944y² = 1. Its smallest solution in positive whole numbers is x = 561,799, y = 18,285.

√944 in geometry and everyday measurements

• 944 square feet is 87.7 m². Laid out as a square — a small house footprint or a lot — it is about 30.72 ft (30 ft 9 in) on a side.
• 944 is not a sum of two whole-number squares — the prime factor 59 (one less than a multiple of 4) appears an odd number of times, which rules that out — so √944 is never the diagonal of a rectangle with whole-number sides. It is, however, the space diagonal of a 4 × 12 × 28 box, because 4² + 12² + 28² = 944.
• Since √944 = 4√59, a length of √944 is exactly 4 copies of the length √59 laid end to end.

Square roots near √944 and related roots

• The cube root of 944 is about 9.809736.
• Because 944 = 4 × 236, the root is twice √236: 2 × 15.362291 ≈ 30.724583.

Need a different value? Use the Square root calculator, or browse the Square roots 1–1,000.