It asks for the number that, when raised to the power of 2, equals 5209.
What is the Square Root of 5209?
The square root of 5209 is 72.1734023031. Calculate another value or review the exact form, nearby perfect powers, and verification.
Answer
Square Root√5209 = 72.1734023031
CalculatedNon-perfect squareIrrational
Exact form√5209
Perfect squareNo
Number typeIrrational
Verification72.17340230312 ≈ 5209
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How the answer is calculated
We solve x2 = 5209. The resulting value is x = 72.1734023031.
Verification: 72.17340230312 ≈ 5209.
Simplified radical form
The square root of 5209 in simplified radical form is √5209.
There are no square factors that can be taken outside the radical, so √5209 is already in simplest radical form.
Nearest Perfect squares
| Position | Base | Value |
|---|---|---|
| Lower or equal | 72 | 5184 |
| Upper or equal | 73 | 5329 |
Nearby square roots
Number properties
Is 5209 a perfect square?
No. Its square root is not a whole number.
Is the square root rational or irrational?
√5209 is irrational because 5209 is not a perfect square.
Visual guide
Square Root function graph
See how the result changes as the input moves across positive and negative values. Square roots are shown for non-negative inputs; cube roots continue through negative inputs.
Common questions
Frequently asked questions
The decimal answer is rounded for display; the radical form remains exact.
Yes. Enter any supported number in the calculator above and select Calculate.