Square Root Calculator
Find the square root of a number and its simplified radical form.
Results update as you type.
About this calculator
A square root calculator gives the principal (positive) square root of a number, plus its simplified radical form and whether the number is a perfect square. Enter any non-negative number to see both the decimal value and the exact radical.
The simplified radical is found by pulling the largest perfect-square factor outside the root sign. For √72, the largest perfect square dividing 72 is 36, so √72 = √(36 × 2) = 6√2 — an exact form, unlike the rounded decimal 8.485. When the number is itself a perfect square, such as 36, the root is a whole number (6) and the tool flags it as a perfect square.
Square roots appear in the Pythagorean theorem, the distance formula, standard deviation and quadratic equations. Note that every positive number has two square roots, one positive and one negative; this tool returns the principal positive root, and negative inputs have no real square root.
Frequently asked questions
What is a simplified radical?
It rewrites a root by factoring out the largest perfect square. √72 = √(36×2) = 6√2, which is exact, unlike the rounded decimal 8.485.
Is the square root of a number always positive?
Every positive number has two square roots, one positive and one negative. This tool returns the principal (positive) root, which is the standard √ result.
What is the square root of 72?
It is about 8.485, and its exact simplified form is 6√2.
What is a perfect square?
A whole number whose square root is also a whole number, such as 36 (√36 = 6). The tool tells you whether your number qualifies.
Can I take the square root of a negative number?
Not within the real numbers — negative inputs have no real square root. You would need complex numbers, where √−4 = 2i.
Why show a simplified radical instead of a decimal?
The radical form is exact. 6√2 is precise, while 8.485 is a rounded approximation that loses accuracy in further calculations.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/square-root/curl
curl "https://calculator.free/api/v1/square-root/?value=72"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/square-root/?" + new URLSearchParams({
"value": "72"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.