Exact
√2
Square Root of 2
Answer
The square root of 2 is 1.4142135624. This is an irrational number — its decimal expansion goes on forever.
Decimal
1.4142135624
Formula
√2 = 1.4142135624
Worked steps
1
Definition
The square root of 2 is the non-negative number that, when multiplied by itself, gives 2. Check: 1.4142135624 × 1.4142135624 ≈ 2 (the squared product equals 2 to the precision shown).
2
Calculator method
Press the √ button, type 2, press =. Result: 1.4142135624.
3
Estimation
2 sits between 1 and 4, so √2 is between 1 and 2. Refining gives 1.4142135624.
About this value
The square root of 2 is the irrational number 1.4142135624. √2 appears in geometry (diagonal of a unit square) and trigonometry (sin 45° = √2/2).
Frequently asked questions
What is square root of 2?
Square Root of 2 equals √2 as an exact value, or 1.4142135624 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
How do I compute it without a calculator?
Use the estimate-and-refine method. For 2, find two perfect squares it sits between, then narrow down. Or use the long-division algorithm taught in school for square roots.
Is the square root rational or irrational?
Irrational. The decimal expansion never terminates and never repeats. Square roots of non-perfect-square integers are always irrational.
How do I simplify a square root?
Find the largest perfect-square factor of the number, take its root out, leave the rest under the radical. Example: √72 = √(36 × 2) = 6√2. If the input is already a perfect square, the root is a clean integer.