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Square Root Calculator

Calculate square roots.

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What is a Square Root Calculator?

A square root calculator finds the principal square root of any non-negative number. It is essential for solving quadratic equations, geometry problems, and many scientific calculations.

How to calculate a square root manually (the formula)

The square root of x is a number r such that r2 = x. For perfect squares like 100, √100 = 10. For non-perfect squares, use estimation: find the two nearest perfect squares and interpolate.

Example calculation

√100 = 10 because 10 × 10 = 100. √50 ≈ 7.07 because 7 × 7 = 49 and 8 × 8 = 64, so √50 is about 7.07.

Common mistakes

  • Forgetting the principal root is non-negative — √100 = 10, not ±10. Both 10 and −10 are square roots, but the radical symbol denotes the principal (positive) root.
  • Taking square root of negative numbers — The square root of a negative number is imaginary, not real.
  • Confusing square root with division by 2 — √x is NOT x / 2. For example, √100 = 10, but 100 / 2 = 50.

Frequently asked questions

What is a square root?

A value that when multiplied by itself gives the number.

How do you calculate a square root by hand?

Estimate between perfect squares.

What is the square root symbol?

√ (radical sign).

Can you take the square root of a negative number?

Yes, it gives an imaginary number (i).

What is a perfect square?

A number with an integer square root.

Is the square root of 2 rational?

No, it is irrational.