Square Root Calculator
Find the square root of any number — the simplified radical form with steps, plus the decimal value. Free in your browser.
Calculate a square root
How to simplify a square root
Find the largest perfect square that divides the number, then take its root outside the radical. Example: √72 — the largest perfect square dividing 72 is 36, so √72 = √(36 × 2) = 6√2 (about 8.4853).
Worked examples
Example 1 — √50. The largest perfect square dividing 50 is 25. √50 = √(25 × 2) = 5√2 (about 7.0711).
Example 2 — √48. The largest perfect square dividing 48 is 16. √48 = √(16 × 3) = 4√3 (about 6.9282).
Example 3 — √98. The largest perfect square dividing 98 is 49. √98 = √(49 × 2) = 7√2 (about 9.8995).
Example 4 — √75. The largest perfect square dividing 75 is 25. √75 = √(25 × 3) = 5√3 (about 8.6603).
Perfect squares worth remembering
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. If your number is one of these, its square root is a whole number: √144 = 12.
Frequently Asked Questions
What is a square root? The square root of a number is the value that, multiplied by itself, gives the number. For example, the square root of 25 is 5, because 5 × 5 = 25.
What does it mean to simplify a square root? Pulling out the largest perfect square factor. For example, √72 = √(36 × 2) = 6√2, because 36 is the largest perfect square dividing 72.
What is the square root of a negative number? Real square roots of negative numbers do not exist. This calculator works with zero and positive numbers only.
What is the difference between √ and ∛? √ is the square root (the number times itself gives the original). ∛ is the cube root (the number times itself twice). This page handles square roots only.
Why does my answer show a decimal and a radical? Most square roots are irrational — they never end. The radical form (like 6√2) is exact; the decimal (like 8.4853) is rounded for everyday use. Teachers usually want the radical form.
How do I estimate a square root by hand? Find the two perfect squares your number sits between. For √50: 49 < 50 < 64, so the answer is just above 7 — the calculator gives 7.0711.
Is this calculator free? Yes. It runs in your browser; nothing is uploaded.
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Educational tool only. For schoolwork, always check your teacher's required format.