Square Root Calculator
Calculate square roots and cube roots with simplified radical form (√48 = 4√3), perfect-square detection and a nearby perfect squares table.
About the Square Root Calculator
This square root calculator gives you more than a decimal answer. Enter any number and you get its square root and cube root, whether it is a perfect square, and — for whole numbers — the simplified radical form that math teachers ask for: √48 = 4√3, √72 = 6√2, √200 = 10√2. A table of nearby perfect squares helps you place the answer between two whole numbers.
Radical simplification works by pulling out the largest perfect-square factor: 48 = 16 × 3, and since √16 = 4, √48 = 4√3. The calculator factors this automatically for any integer up to a billion. Negative numbers are handled honestly too: they have no real square root (the result is imaginary), but they do have a real cube root, which the tool still shows.
Students simplifying radicals for algebra homework, anyone checking whether a number is a perfect square, and practical users computing side lengths from areas (a 200 m² square plot has sides of √200 ≈ 14.14 m) all get instant answers with no signup.
How to Use the Square Root Calculator
- 1Type any number — positive, negative, whole or decimal.
- 2Read the square root and cube root instantly.
- 3For whole numbers, check the simplified radical form and the perfect-square flag.
- 4Use the nearby perfect squares table to see where your number falls.
Frequently Asked Questions
How do I simplify a square root like √48?
Find the largest perfect square that divides the number. 48 = 16 × 3, so √48 = √16 × √3 = 4√3. Similarly √72 = √(36 × 2) = 6√2. The calculator finds the factorisation automatically and shows the simplified form whenever one exists.
What is the square root of a negative number?
There is no real square root of a negative number — √(−9) is the imaginary number 3i. Cube roots are different: ∛(−27) = −3 is perfectly real, because a negative times itself three times stays negative. The calculator shows the cube root even when the square root does not exist.
How can I tell if a number is a perfect square?
Its square root is a whole number. 144 is a perfect square because √144 = 12 exactly; 145 is not, because √145 ≈ 12.042. The calculator flags perfect squares and lists the nearby ones (121, 144, 169...) so you can see the gaps.
How do I estimate a square root without a calculator?
Bracket it between perfect squares. For √50: since 49 < 50 < 64, the root is between 7 and 8, and much closer to 7 — about 7.07. The nearby perfect squares table in this tool is designed exactly for this technique, which is also common in exams that ban calculators.
What is the difference between square root and cube root?
The square root asks what number times itself gives x (√64 = 8 because 8 × 8 = 64); the cube root asks what number used three times gives x (∛64 = 4 because 4 × 4 × 4 = 64). Square roots come from areas, cube roots from volumes — a 64 m³ cubic tank has 4 m edges.