Square Root Calculator › Square root of 38

Square Root of 38

√38 ≈ 6.164414

38 is not a perfect square, so √38 is an irrational number that is approximately 6.164414. In simplified radical form, √38 = √38.

√38 lies between √36 = 6 and √49 = 7.

Number38
Square root (decimal)6.164414
Simplified radical√38
Perfect square?No
Rational?No

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Prime factorization of 38

38 = 2 × 19. This is what determines the simplified radical: for √38 you pull out one copy of any prime that appears twice.

No prime appears twice, so nothing can be taken out — √38 is already in simplest radical form as √38.

Estimating √38 by hand

√38 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 38 ÷ the guess:

StepEstimate
Start6
Step 16.166667
Step 26.164414
Step 36.164414

After 3 steps the estimate is 6.164414, matching √38 ≈ 6.164414.

Nearby square roots

√36 · √37 · √39 · √40

← Square root of 37 | Square root of 39 →

Frequently asked questions

Is 38 a perfect square?

No, 38 is not a perfect square, so its square root is irrational and approximately 6.164414.

What is the square root of 38 in simplest radical form?

√38 = √38 in simplest radical form.