Square Root Calculator

Square Root Calculator

Calculate square roots and squares instantly. Perfect for algebra, geometry, engineering, and everyday math problems.

Last updated: April 2026 | By Patchworkr Team

Square root
Enter a number to calculate

What Is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 × 4 = 16.

The square root symbol is √. So √16 = 4. Every positive number has two square roots: one positive and one negative. This calculator returns the positive (principal) square root.

Perfect squares (like 1, 4, 9, 16, 25, etc.) have whole number square roots. Most other numbers have irrational square roots with infinite decimal places (like √2 ≈ 1.414...).

How To Calculate Square Roots and Squares

Square root definition

If x² = y, then √y = x

Square root reverses squaring. If you know the square, you can find the original number.

Squaring a number

x² = x × x

Multiply a number by itself to get its square.

Perfect squares

1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25...

These have exact whole-number square roots.

Worked Example: Finding √144

What number multiplied by itself gives 144?

√144 = ?
12 × 12 = 144
Therefore, √144 = 12
√144 = 12

Perfect Squares (1 to 16)

NumberCalculationSquare
11²1
22²4
33²9
44²16
55²25
66²36
77²49
88²64
99²81
1010²100
1111²121
1212²144
1313²169
1414²196
1515²225
1616²256

Frequently Asked Questions

Can you take the square root of a negative number?

Not in real numbers. Square roots of negatives produce imaginary numbers (involving i).

What does √2 equal?

√2 ≈ 1.414. It's an irrational number—its decimal never ends or repeats.

Why are perfect squares important?

They appear in geometry, algebra, and provide easy reference points for estimating other square roots.

Is √16 the same as -4?

No. The square root symbol √ always means the positive root. √16 = 4 (not -4).

How do I estimate √50?

Find nearby perfect squares: 7² = 49 and 8² = 64, so √50 is between 7 and 8 (≈ 7.07).

What's the relationship between √ and ²?

They're inverses. If x² = y, then √y = x. Square root undoes squaring.

Are there square roots other than positive and negative?

In real numbers, no. But in complex numbers, yes—they involve the imaginary unit i.

How many square roots does a positive number have?

Technically two: one positive and one negative. The √ symbol typically refers to the positive root.

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