Square Root Calculator: Finding and Simplifying Square Roots
The square root is one of the most fundamental operations in mathematics. From geometry (side length from area) to statistics (standard deviation), square roots appear everywhere...
Square Root Calculator
Calculate square roots with exact simplification
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Formula
Formula
√x = x^(1/2); √(a×b) = √a × √b
Square root is the inverse of squaring. Simplification extracts perfect square factors from the radicand.
How to Calculate Manually
- 1 Enter a non-negative number
- 2 Calculator computes the principal square root
- 3 Also shows the negative root (±)
- 4 Simplifies the radical by extracting perfect squares
- 5 Shows both decimal and exact forms
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Reference Table
| Number | Square Root | Simplified | Perfect Square? |
|---|---|---|---|
| 1 | 1 | 1 | Yes |
| 4 | 2 | 2 | Yes |
| 9 | 3 | 3 | Yes |
| 16 | 4 | 4 | Yes |
| 25 | 5 | 5 | Yes |
| 72 | 8.485 | 6√2 | No |
| 100 | 10 | 10 | Yes |
| 200 | 14.142 | 10√2 | No |
Frequently Asked Questions
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What is a square root?
-
How do you simplify square roots?
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What about negative numbers?
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