What are perfect squares?

Perfect squares are integers that have exact integer square roots: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144... Their square roots are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...

Can you take the square root of a negative number?

Not in real numbers. The square root of a negative number is an imaginary number (using i, where i = √-1). For example, √-9 = 3i. This is used in complex number mathematics and electrical engineering.

What is the Pythagorean theorem?

The Pythagorean theorem states a² + b² = c², where c is the hypotenuse (longest side) of a right triangle. To find the hypotenuse: c = √(a² + b²). Square roots are essential for this fundamental geometry calculation.

How do I estimate a square root without a calculator?

Find the nearest perfect squares. For √50: 7² = 49, 8² = 64. So √50 is between 7 and 8, closer to 7. More precisely: 7.07² ≈ 50. You can refine using: √n ≈ a + (n-a²)/(2a) where a is the nearest perfect root.

Square Root Calculator — Free & Instant

The Square Root Calculator finds the square root, cube root, or any nth root of a number instantly. Square roots are fundamental to mathematics — they appear in the Pythagorean theorem, quadratic equations, physics formulas, geometry, and statistics. Enter any positive number and get the exact decimal result immediately. You can also calculate cube roots (∛) and higher roots for scientific and engineering calculations.

Number

Root Type

Frequently Asked Questions

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots (positive and negative), but by convention we use the positive (principal) root.

Related Calculators

📐Percentage Calculator 📐Fraction Calculator 📐Average Calculator