Square Root of 620

√620 at a glance

Exact value

2√155

Decimal (10 places)

24.8997991960

Rounded

24.9 · 24.90 · 24.900

Perfect square?

No — between 24² and 25²

Rational?

Irrational

Both square roots

±24.899799

Prime factorization

2² × 5 × 31

Cube root

8.527019

How to simplify √620

Look for the largest perfect square that divides 620. Here it is 4 (2²), because 620 = 4 × 155 and 155 has no square factor left:

The prime factorization tells the same story: 620 = 2² × 5 × 31. Each pair of equal primes leaves the radical as one factor, so 2 comes out and 5 × 31 stays inside.

Check: (2√155)² = 2² × 155 = 4 × 155 = 620. As a decimal, 2√155 = 2 × 12.449899598 ≈ 24.8997991960.

Where √620 sits between perfect squares

576 = 24² and 625 = 25² are the nearest perfect squares, so √620 lies between 24 and 25. 620 is 44 above 576 and 5 below 625, so the root is closer to 25.

• Straight line between 576 and 625: 24.8980 (0.01% low)
• Tangent from 24, i.e. 24 + 44 ÷ 48: 24.9167 (0.07% high)
• Tangent from 25, i.e. 25 − 5 ÷ 50: 24.9000 (0% high)

For √620 the tangent at 25 wins, missing by only 0.0002. Tangent estimates shine when the number sits close to a perfect square — here 620 is just 5 below 625.

Finding √620 with the Babylonian method

Picture a rectangle with an area of 620 and one side x; the other side must be 620 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √620.

Start from the nearest whole number, 25 (25² = 625):

The count of correct decimals went 3, 9 and all 10 over 3 steps — roughly doubling each time — until the guess matched √620 = 24.8997991960 to every decimal shown.

√620 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √620 the pattern is [24; 1, 8, 1, 48] with the block of 4 terms after the semicolon repeating forever. A pattern that never ends is one more proof that √620 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 − 620y² = 1. Its smallest solution in positive whole numbers is x = 249, y = 10.

√620 in geometry and everyday measurements

• A square garage floor of 620 square feet measures about 24.9 ft (24 ft 11 in) per side, and its corner-to-corner diagonal is √1240 ≈ 35.2 ft.
• 620 is not a sum of two whole-number squares — the prime factor 31 (one less than a multiple of 4) appears an odd number of times, which rules that out — so √620 is never the diagonal of a rectangle with whole-number sides. It is, however, the space diagonal of a 6 × 10 × 22 box, because 6² + 10² + 22² = 620.
• Since √620 = 2√155, a length of √620 is exactly 2 copies of the length √155 laid end to end.

Square roots near √620 and related roots

• The cube root of 620 is about 8.527019.
• Because 620 = 4 × 155, the root is twice √155: 2 × 12.4499 ≈ 24.899799.

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