Square Root of 704

√704 at a glance

Exact value

8√11

Decimal (10 places)

26.5329983228

Rounded

26.5 · 26.53 · 26.533

Perfect square?

No — between 26² and 27²

Rational?

Irrational

Both square roots

±26.532998

Prime factorization

2⁶ × 11

Cube root

8.895920

How to simplify √704

Look for the largest perfect square that divides 704. Here it is 64 (8²), because 704 = 64 × 11 and 11 has no square factor left:

The prime factorization tells the same story: 704 = 2⁶ × 11. Each pair of equal primes leaves the radical as one factor, so 2³ comes out and 11 stays inside.

704 has 3 square factors (4, 16 and 64). Starting with a smaller one still works but takes more rounds: √704 = 2√176, and √176 can be simplified again. Using 64 straight away finishes in one step.

Check: (8√11)² = 8² × 11 = 64 × 11 = 704. As a decimal, 8√11 = 8 × 3.3166247904 ≈ 26.5329983228.

Where √704 sits between perfect squares

676 = 26² and 729 = 27² are the nearest perfect squares, so √704 lies between 26 and 27. 704 is 28 above 676 and 25 below 729, so the root is closer to 27.

• Straight line between 676 and 729: 26.5283 (0.02% low)
• Tangent from 26, i.e. 26 + 28 ÷ 52: 26.5385 (0.02% high)
• Tangent from 27, i.e. 27 − 25 ÷ 54: 26.5370 (0.02% high)

For √704 the tangent at 27 wins, missing by only 0.004. Tangent estimates shine when the number sits close to a perfect square — here 704 is just 25 below 729.

Finding √704 with the Babylonian method

Picture a rectangle with an area of 704 and one side x; the other side must be 704 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √704.

Start from the nearest whole number, 27 (27² = 729):

The count of correct decimals went 2, 6 and all 10 over 3 steps — roughly doubling each time — until the guess matched √704 = 26.5329983228 to every decimal shown.

√704 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √704 the pattern is [26; 1, 1, 7, 13, 7, 1, 1, 52] with the block of 8 terms after the semicolon repeating forever. A pattern that never ends is one more proof that √704 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 − 704y² = 1. Its smallest solution in positive whole numbers is x = 79,201, y = 2,985.

√704 in geometry and everyday measurements

• 704 square feet is 65.4 m². Laid out as a square — a small house footprint or a lot — it is about 26.53 ft (26 ft 6 in) on a side.
• 704 is not a sum of two whole-number squares — the prime factor 11 (one less than a multiple of 4) appears an odd number of times, which rules that out — so √704 is never the diagonal of a rectangle with whole-number sides. It is, however, the space diagonal of a 8 × 8 × 24 box, because 8² + 8² + 24² = 704.
• Since √704 = 8√11, a length of √704 is exactly 8 copies of the length √11 laid end to end.

Square roots near √704 and related roots

• The cube root of 704 is about 8.895920.
• Because 704 = 4 × 176, the root is twice √176: 2 × 13.266499 ≈ 26.532998.

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