It asks for the number that, when raised to the power of 2, equals 20164.
What is the Square Root of 20164?
The square root of 20164 is 142. Calculate another value or review the exact form, nearby perfect powers, and verification.
Answer
Square Root√20164 = 142
ExactPerfect squareRational
Exact form142
Perfect squareYes
Number typeRational
Verification1422 ≈ 20164
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How the answer is calculated
We solve x2 = 20164. The resulting value is x = 142.
Verification: 1422 ≈ 20164.
Simplified radical form
The square root of 20164 in simplified radical form is 142.
There are no square factors that can be taken outside the radical, so 142 is already in simplest radical form.
Nearest Perfect squares
| Position | Base | Value |
|---|---|---|
| Lower or equal | 142 | 20164 |
| Upper or equal | 142 | 20164 |
Nearby square roots
Number properties
Is 20164 a perfect square?
Yes. Its square root is the whole number 142.
Is the square root rational or irrational?
142 is rational because it is a whole number.
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 answer is exact because this input is a perfect square.
Yes. Enter any supported number in the calculator above and select Calculate.