Square Root Calculator
Calculate the square root (√) of any number. Supports both positive and negative numbers (complex results shown).
Square Root
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How to use the Square Root Calculator
- Enter a positive number.
- Click Calculate to see its square root.
- Check whether the number is a perfect square.
- Use the cube root or exponent calculators for other roots and powers.
Formula used
√x = y, where y × y = x
Worked example
Examples
√144 = 12 (perfect square)
√50 ≈ 7.0711
√2 ≈ 1.41421
Estimating square roots by hand
Find the two perfect squares around your number. √50 lies between √49 = 7 and √64 = 8, closer to 7. A quick refinement: 7 + (50 − 49) ÷ (2 × 7) ≈ 7.07. Simplifying surds also helps: √50 = √(25 × 2) = 5√2.
Perfect squares 1–20
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
Tips for accurate results
- Square roots of negative numbers are not real; they are imaginary (for example √−4 = 2i).
- Every positive number has two square roots, + and −; the calculator shows the positive one.
- For areas, the square root gives the side of a square: a 400 sq ft square room is 20 ft per side.
Frequently Asked Questions
About 1.41421356.
Both 5 and −5 squared give 25, but √25 conventionally means the positive root, 5.
Take the square root of the area.
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Content reviewed by Vinod, Easy Smart Calculator · Last updated October 2026
√x = y where y² = x