What is the square root of 30?

The square root of 30 is sqrt30. In decimal: sqrt(30) approximately 5.4772255751 This is irrational — the decimal never terminates or repeats. sqrt(30)=5.47722...=sqrt(2)*sqrt(3)*sqrt(5). No repeated prime factors so stays as sqrt(30).

Is 30 a perfect square?

No. 30 is not a perfect square. 5 squared = 25 and 6 squared = 36. Since 30 falls between these, sqrt(30) is not an integer. Nearest perfect squares: 25 (= 5 squared) and 36 (= 6 squared).

How do you simplify sqrt(30)?

sqrt(30) simplifies to sqrt30. Method: prime factorisation of 30 = 2 x 3 x 5. Since no factor repeats, sqrt(30) cannot be simplified further.

What is sqrt(30) squared?

(sqrt(30)) squared = 30. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(30)) squared = 30 always.

What is the difference between square root and squaring?

Squaring 30: 30 squared = 900 (multiply 30 by itself). Square root of 30: sqrt(30) = sqrt30 approximately 5.4772. They are inverse operations: sqrt(30) squared = 30 and sqrt(30 squared) = 30 (for non-negative numbers).

Square Root of 30 — sqrt(30) = sqrt30

The square root of 30 is sqrt30. In decimal form, sqrt(30) approximately 5.477226 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√30 = ?

SQUARE ROOT OF 30

√30

≈ 5.4772255751

Irrational — cannot be expressed as a fraction

Exact form

√30

Decimal (4dp)

5.4772

Decimal (10dp)

5.4772255751

Is perfect sq?

√30 ²

30 ✓

Between

5 and 6

DECIMAL PRECISION

√30 ≈ 5.4772255751

STEP-BY-STEP

Prime factorisation: 30 = 2 × 3 × 5

Simplified radical form: √30

5² = 25 < 30 < 36 = 6² → lies between 5 and 6

√30 ≈ 5.4772255751...

FUN FACT

sqrt(30)=5.47722...=sqrt(2)*sqrt(3)*sqrt(5). No repeated prime factors so stays as sqrt(30).

NUMBER LINE (√30 ≈ 5.4772)

√30

SQUARE WITH AREA = 30

Area = 30

√30

≈ 5.477

√30 ≈ 5.477

NEARBY PERFECT SQUARES

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

√64= 88² = 64

SQUARE ROOT LAWS

√30 × √30= 30

(√30)²= 30

√(30 × 4)= 2√30 ≈ 10.9545

√(30/4)= √30/2 ≈ 2.7386

√30 × √31≈ 30.4959

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HOW TO CALCULATE

1
Find the prime factorisation of 30: 30 = 2 x 3 x 5. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt30. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(30) between integers: 5 squared = 25 and 6 squared = 36. Since 25 < 30 < 36, sqrt(30) lies between 5 and 6.
4
Calculate decimal: sqrt(30) approximately 5.4772255751. Verify by squaring: (5.477226) squared approximately 30.0 = 30.

WORKED EXAMPLE

sqrt(30): not a perfect square. Factorisation: 30 = 2 x 3 x 5. Simplified: sqrt30. Decimal: sqrt(30) approximately 5.4772255751.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √17 √18 √19 √20 √21 √22 √23 √24 √25 √26 √27 √28 √29

Bold bordered = perfect squares (exact integer result)

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Last updated: April 28, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.