Exact
√3
Square Root of 3
Answer
The square root of 3 is 1.7320508076. This is an irrational number — its decimal expansion goes on forever.
Decimal
1.7320508076
Formula
√3 = 1.7320508076
Worked steps
1
Definition
The square root of 3 is the non-negative number that, when multiplied by itself, gives 3. Check: 1.7320508076 × 1.7320508076 ≈ 3 (the squared product equals 3 to the precision shown).
2
Calculator method
Press the √ button, type 3, press =. Result: 1.7320508076.
3
Estimation
3 sits between 1 and 4, so √3 is between 1 and 2. Refining gives 1.7320508076.
About this value
The square root of 3 is the irrational number 1.7320508076. √3 appears in 30–60–90 triangle geometry — sin 60° = √3/2.
Frequently asked questions
What is square root of 3?
Square Root of 3 equals √3 as an exact value, or 1.7320508076 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 3, 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.