Can I find the square root of any number — including large numbers and decimals?

Yes. This calculator works with any non-negative number: - Small integers: 2, 7, 15 - Perfect squares: 100, 225, 10000 - Large numbers: 1000000, 999999 - Decimals: 2.5, 0.25, 3.14159 - Fractions as decimals: 0.5 (= sqrt(0.5) approx 0.7071) For negative numbers, the result is imaginary (i*sqrt(|n|)) — the calculator flags this clearly. Examples: sqrt(0.25) = 0.5 (exact) sqrt(2.5) approx 1.58113 sqrt(1000000) = 1000 (exact, 1000 squared = 1000000)

What is a simplified radical form?

Simplified radical form means extracting any perfect square factors from under the radical sign. Method: find the prime factorisation and pull out pairs. Examples: sqrt(8) = sqrt(4*2) = 2*sqrt(2) sqrt(12) = sqrt(4*3) = 2*sqrt(3) sqrt(18) = sqrt(9*2) = 3*sqrt(2) sqrt(20) = sqrt(4*5) = 2*sqrt(5) sqrt(50) = sqrt(25*2) = 5*sqrt(2) sqrt(72) = sqrt(36*2) = 6*sqrt(2) When no perfect square factor exists (e.g. sqrt(7), sqrt(11), sqrt(13)), the radical is already in simplest form.

How do you find the square root of a decimal number?

For decimal inputs, the calculator uses the mathematical definition: sqrt(x) is the positive number y such that y squared = x. Examples: sqrt(0.25) = 0.5 (since 0.5 squared = 0.25) sqrt(2.25) = 1.5 (since 1.5 squared = 2.25) sqrt(0.5) approx 0.70710678 sqrt(3.14) approx 1.77200 Tip: fractions with perfect square numerator and denominator have exact decimal square roots: sqrt(1/4) = 1/2 = 0.5 sqrt(9/25) = 3/5 = 0.6 sqrt(16/49) = 4/7 approx 0.571

What is the square root of a negative number?

The square root of a negative number is imaginary — it involves the imaginary unit i, defined as i = sqrt(-1). sqrt(-1) = i sqrt(-4) = 2i sqrt(-7) approx 2.6457i sqrt(-n) = i * sqrt(n) Imaginary numbers are part of complex numbers (a + bi) and appear in: - Electrical engineering (AC circuits) - Quantum mechanics - Signal processing - Solutions to quadratic equations with negative discriminants For real-world calculations, negative inputs typically indicate an error in the problem setup.

How is the shareable URL useful?

The SHARE button generates a URL with your number encoded as a parameter: https://eaglecalculator.com/math/algebra/square-root-mega?n=72 Anyone who opens this link sees sqrt(72) = 6*sqrt(2) approx 8.4852 automatically loaded — no need to type anything. Useful for: - Sending a specific square root to a student or colleague - Bookmarking a frequently needed value - Embedding a specific square root in a message or document The URL always reflects the current number. Sharing after changing the number shares the new value.

Square Root Mega — Find Square Root of Any Number

The Square Root Mega finds the square root of any number instantly — integers, decimals, or large numbers. Enter any value and see the exact form (integer for perfect squares, simplified radical like 2*sqrt(5) for others), decimal to up to 20 places with adjustable precision, prime factorisation, a ...

√ ANY NUMBER

ENTER ANY NUMBER

√

QUICK SELECT

Bold-bordered = perfect squares

√2 =

√2

≈ 1.4142135624

Irrational — decimal never ends or repeats

DECIMAL PRECISION

√2 ≈ 1.4142135624

Exact form

√2

Decimal (6dp)

1.414214

Is perfect sq?

(√2)²

2 ✓

Between

1 and 2

Factors

STEPS

Factorisation: 2 = 2

Simplified radical: √2

√2 ≈ 1.4142135624

NUMBER LINE (√2 ≈ 1.4142)

1.4142

SQUARE WITH AREA = 2

Area = 2

√2

≈ 1.414

√2 ≈ 1.414

NEARBY PERFECT SQUARES

√0= 00² = 0

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

Click any row to load that square

SQUARE ROOT LAWS

√2 × √2= 2

(√2)²= 2

√(2×4)= 2√2 ≈ 2.8284

√(2/4)= √2/2 ≈ 0.7071

√2 × √3≈ 2.4495

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type any number into the large input box — integers, decimals, or large numbers all work. The square root is computed instantly. Use the quick-select buttons to jump to common values.
2
Perfect squares (1, 4, 9, 16, 25...) show an exact green integer answer. All other numbers show the simplified radical form (e.g. 2*sqrt(5) for sqrt(20)) and a decimal approximation.
3
Adjust decimal precision from 4 to 20 decimal places using the precision buttons. The full decimal string is shown below — useful for copying into calculations.
4
Click COPY to copy the result as text (e.g. 'sqrt(2) = sqrt(2) approx 1.4142135623'). Click SHARE to copy a direct URL that auto-loads your number for anyone you send it to.
5
The nearby perfect squares panel shows clickable rows — click any to instantly switch to that number. The square visualisation shows a square whose area equals your number, with side length = the square root.

WORKED EXAMPLES

sqrt(2): not a perfect square. Factorisation: 2 = 2 (prime). Simplified: sqrt(2). Decimal: sqrt(2) approx 1.4142135623. sqrt(72): factorisation: 72 = 2x2x2x3x3 = 4x4x... wait: 72 = 36x2. Simplified: 6*sqrt(2) approx 8.4852813742. sqrt(0.25): 0.5 squared = 0.25. Perfect decimal square. sqrt(0.25) = 0.5 (exact). sqrt(1000000): 1000 squared = 1000000. sqrt(1000000) = 1000 (exact).

FREQUENTLY ASKED QUESTIONS

INDIVIDUAL SQUARE ROOT PAGES (1–30)

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √17 √18 √19 √20 √21 √22 √23 √24 √25 √26 √27 √28 √29 √30

Bold = perfect squares (exact integer result)

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Last updated: April 28, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.