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What is the Square Root of 21213?

The square root of 21213 is 145.6468331273. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√21213 = 145.6468331273
CalculatedNon-perfect squareIrrational
Exact form√21213
Perfect squareNo
Number typeIrrational
Verification145.64683312732 ≈ 21213

On this page

How the answer is calculated

We solve x2 = 21213. The resulting value is x = 145.6468331273.

Verification: 145.64683312732 ≈ 21213.

Simplified radical form

The square root of 21213 in simplified radical form is 3√2357.

This is equivalent to √21213, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal14521025
Upper or equal14621316

Nearby square roots

NumberSquare root
√21210145.636533878
√21211145.639967042
√21212145.6434001251
√21213145.6468331273
√21214145.6502660485
√21215145.6536988888
√21216145.6571316483

Number properties

Is 21213 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√21213 is irrational because 21213 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

It asks for the number that, when raised to the power of 2, equals 21213.