Square Root of 695

√695 at a glance

Exact value

√695

Decimal (10 places)

26.3628526529

Rounded

26.4 · 26.36 · 26.363

Perfect square?

No — between 26² and 27²

Rational?

Irrational

Both square roots

±26.362853

Prime factorization

5 × 139

Cube root

8.857849

How to simplify √695

The prime factorization of 695 is 5 × 139. Every prime appears only once, so there is no pair to bring outside the radical — √695 is already in simplest form (a "square-free" radicand).

A whole number has a rational square root only when every prime in its factorization appears an even number of times. In 695, 5 and 139 appear an odd number of times, so √695 is irrational and 26.3628526529 is a rounded value.

Where √695 sits between perfect squares

676 = 26² and 729 = 27² are the nearest perfect squares, so √695 lies between 26 and 27. 695 is 19 above 676 and 34 below 729, so the root is closer to 26.

• Straight line between 676 and 729: 26.3585 (0.02% low)
• Tangent from 26, i.e. 26 + 19 ÷ 52: 26.3654 (0.01% high)
• Tangent from 27, i.e. 27 − 34 ÷ 54: 26.3704 (0.03% high)

For √695 the tangent at 26 wins, missing by only 0.0025. Tangent estimates shine when the number sits close to a perfect square — here 695 is just 19 above 676.

Finding √695 with the Babylonian method

If a guess is too big, 695 ÷ x is too small by about the same amount, so their average lands much closer. In fact an error of e shrinks to roughly e² ÷ (2√695) in one step.

Start from the nearest whole number, 26 (26² = 676):

The count of correct decimals went 2, 6 and all 10 over 3 steps — roughly doubling each time — until the guess matched √695 = 26.3628526529 to every decimal shown.

√695 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √695 the pattern is [26; 2, 1, 3, 10, 3, 1, 2, 52] with the block of 8 terms after the semicolon repeating forever. A pattern that never ends is one more proof that √695 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 − 695y² = 1. Its smallest solution in positive whole numbers is x = 33,639, y = 1,276.

√695 in geometry and everyday measurements

• 695 square feet is 64.6 m². Laid out as a square — a small house footprint or a lot — it is about 26.36 ft (26 ft 4 in) on a side.
• 695 is not a sum of two whole-number squares — the prime factor 139 (one less than a multiple of 4) appears an odd number of times, which rules that out — so √695 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 √695 as its space diagonal.

Square roots near √695 and related roots

• The cube root of 695 is about 8.857849.
• Squaring undoes the root: (√695)² = 695, while 695² = 483,025 — the number whose square root is 695.

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