RootLab

Square Root Calculator

√n and n² together.

Number

Square root

√n

Squared: 20,736

What you entered

Number: 144

1
Take the square root
√144= 12
2
Check: square it back
12²= 144

Result

Square root: 12

The square root of 144 is 12.

Square roots of common numbers

The square root is the value that multiplied by itself gives the original number. The last column squares the input instead, for comparison.

Number	Square root	Number squared
2	1.414214	4
4	2.000000	16
9	3.000000	81
10	3.162278	100
16	4.000000	256
25	5.000000	625
50	7.071068	2500
100	10.000000	10000
144	12.000000	20736

The square root of 2 at 1.414214 is the number that proved irrational numbers exist - it cannot be written as a fraction, and its discovery reportedly unsettled the Pythagoreans. Perfect squares like 4, 9, 16, 25, 100 and 144 give whole-number roots; everything else gives an unending non-repeating decimal. Note that every positive number technically has two square roots, positive and negative, since both squared give the same result - calculators return the positive one by convention. Negative numbers have no real square root at all.

The inverse of squaring

√n asks 'what number, multiplied by itself, gives n?' — it undoes squaring, which is why negative numbers have no real square root: no real number squared can produce a negative result.

Where it's used

Square roots appear in the Pythagorean theorem, standard deviation, physics equations for speed and energy, and any time you're reversing an area calculation to find a side length.

Frequently asked questions

How do I calculate a square root?

√n is the number that, multiplied by itself, gives n. √49 = 7, √100 = 10, √2 ≈ 1.414. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) have whole-number roots; others are irrational (infinite non-repeating decimals).

Can you take the square root of a negative number?

Not in real numbers. No real number squared gives a negative result. In complex numbers, √(−1) = i (the imaginary unit), and √(−9) = 3i. Real-world measurements always use real square roots.

How do I simplify a square root?

Factor out perfect squares: √72 = √(36×2) = 6√2. √200 = √(100×2) = 10√2. √48 = √(16×3) = 4√3. Find the largest perfect square factor, take its root out, and leave the rest under the radical.