Maths / Roots
Square Root Calculator
Find the square root, cube root, or any root of a number, as a decimal and in simplified radical form, such as √72 = 6√2.
Square Root Calculator: The root is computed to full precision and snapped to a whole number when it is exact, so ∛27 shows as 3. For whole numbers, the root is also simplified by taking out the largest factor that is a perfect power: 72 = 36 × 2, so √72 = 6√2. Odd roots of negative numbers are negative; even roots of negative numbers are not real numbers. Runs 100% locally in your browser with zero server file uploads.
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√72 = 6√2 ≈ 8.4852813742
Simplified by taking out the largest factor that is a perfect power: 72 = 36 × 2.
Estimating a square root
Find the perfect squares on either side: 50 lies between 49 and 64, so √50 is a little above 7, about 7 + 1/14 ≈ 7.07. One step of Newton's method improves any guess g: take (g + x ÷ g) ÷ 2.
To find the factors that make a radical simplify, use prime factorisation.
Roots as powers
A root is a fractional power: the square root of x is x^(1/2), the cube root x^(1/3). So ⁴√16 = 16^(1/4) = 2, and roots follow the same rules as powers.
How to use it
- Enter the number.
- Choose the root: square, cube, or a higher one.
- Read the simplified radical and the decimal value.
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The calculation runs in your browser.
Related tools
Frequently asked questions
How do I simplify a square root by hand?
Find the largest perfect square that divides the number, take its root outside, and leave the rest inside: √50 = √(25 × 2) = 5√2.
What is the square root of a negative number?
Not a real number: √−9 = 3i, where i is the square root of −1. Cube roots of negatives are real: ∛−8 = −2.
Which numbers are perfect squares?
Squares of whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on; their square roots are whole numbers.
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