Square Root of 244

√244 at a glance

Exact value

2√61

Decimal (10 places)

15.6204993518

Rounded

15.6 · 15.62 · 15.620

Perfect square?

No — between 15² and 16²

Rational?

Irrational

Both square roots

±15.620499

Prime factorization

2² × 61

Cube root

6.248800

How to simplify √244

Look for the largest perfect square that divides 244. Here it is 4 (2²), because 244 = 4 × 61 and 61 has no square factor left:

The prime factorization tells the same story: 244 = 2² × 61. Each pair of equal primes leaves the radical as one factor, so 2 comes out and 61 stays inside.

Check: (2√61)² = 2² × 61 = 4 × 61 = 244. As a decimal, 2√61 = 2 × 7.8102496759 ≈ 15.6204993518.

Where √244 sits between perfect squares

225 = 15² and 256 = 16² are the nearest perfect squares, so √244 lies between 15 and 16. 244 is 19 above 225 and 12 below 256, so the root is closer to 16.

• Straight line between 225 and 256: 15.6129 (0.05% low)
• Tangent from 15, i.e. 15 + 19 ÷ 30: 15.6333 (0.08% high)
• Tangent from 16, i.e. 16 − 12 ÷ 32: 15.6250 (0.03% high)

For √244 the tangent at 16 wins, missing by only 0.0045. Tangent estimates shine when the number sits close to a perfect square — here 244 is just 12 below 256.

Finding √244 with the Babylonian method

Picture a rectangle with an area of 244 and one side x; the other side must be 244 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √244.

Start from the nearest whole number, 16 (16² = 256):

The count of correct decimals went 2, 6 and all 10 over 3 steps — roughly doubling each time — until the guess matched √244 = 15.6204993518 to every decimal shown.

√244 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √244 the pattern is [15; 1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 9, 1, …] with the block of 26 terms after the semicolon repeating forever (only the first 12 of the 26 are shown). A pattern that never ends is one more proof that √244 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 − 244y² = 1. Its smallest solution in positive whole numbers is x = 1,766,319,049, y = 113,076,990.

√244 in geometry and everyday measurements

• A square patio or deck of 244 square feet is about 15.62 ft (15 ft 7 in) on each side, so edging all the way around takes 4 × √244 ≈ 62.5 ft.
• 244 = 10² + 12², so by the Pythagorean theorem √244 is the diagonal of a 10 × 12 rectangle — and the distance between the points (0, 0) and (10, 12) on a grid.
• Since √244 = 2√61, a length of √244 is exactly 2 copies of the length √61 laid end to end.

Square roots near √244 and related roots

• The cube root of 244 is about 6.248800.
• Four times the radicand doubles the root: √976 = 2 × √244 ≈ 31.240999.

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