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What is the Square Root of 45?

The square root of 45 is 6.7082039325. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√45 = 6.7082039325
CalculatedNon-perfect squareIrrational
Exact form√45
Perfect squareNo
Number typeIrrational
Verification6.70820393252 ≈ 45

On this page

How the answer is calculated

We solve x2 = 45. The resulting value is x = 6.7082039325.

Verification: 6.70820393252 ≈ 45.

Simplified radical form

The square root of 45 in simplified radical form is 3√5.

This is equivalent to √45, with perfect-square factors moved outside the radical.

Nearest Perfect squares

PositionBaseValue
Lower or equal636
Upper or equal749

Nearby square roots

NumberSquare root
√426.4807406984
√436.5574385243
√446.6332495807
√456.7082039325
√466.7823299831
√476.8556546004
√486.9282032303

Number properties

Is 45 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√45 is irrational because 45 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 45.