What is the square root of 27?

The square root of 27 is 3sqrt3. In decimal: sqrt(27) approximately 5.1961524227 This is irrational — the decimal never terminates or repeats. sqrt(27)=3*sqrt(3) approximately 5.19615... Simplifies because 27=9*3.

Is 27 a perfect square?

No. 27 is not a perfect square. 5 squared = 25 and 6 squared = 36. Since 27 falls between these, sqrt(27) is not an integer. Nearest perfect squares: 25 (= 5 squared) and 36 (= 6 squared).

How do you simplify sqrt(27)?

sqrt(27) simplifies to 3sqrt3. Method: prime factorisation of 27 = 3 x 3 x 3. Extract pairs of identical factors: result is 3sqrt3.

What is sqrt(27) squared?

(sqrt(27)) squared = 27. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(27)) squared = 27 always.

What is the difference between square root and squaring?

Squaring 27: 27 squared = 729 (multiply 27 by itself). Square root of 27: sqrt(27) = 3sqrt3 approximately 5.1962. They are inverse operations: sqrt(27) squared = 27 and sqrt(27 squared) = 27 (for non-negative numbers).

Square Root of 27 — sqrt(27) = 3sqrt3

The square root of 27 is 3sqrt3. In decimal form, sqrt(27) approximately 5.196152 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√27 = ?

SQUARE ROOT OF 27

3√3

≈ 5.1961524227

Irrational — cannot be expressed as a fraction

Exact form

3√3

Decimal (4dp)

5.1962

Decimal (10dp)

5.1961524227

Is perfect sq?

√27 ²

27 ✓

Between

5 and 6

DECIMAL PRECISION

√27 ≈ 5.1961524227

STEP-BY-STEP

Prime factorisation: 27 = 3 × 3 × 3

Simplified radical form: 3√3

5² = 25 < 27 < 36 = 6² → lies between 5 and 6

√27 ≈ 5.1961524227...

FUN FACT

sqrt(27)=3*sqrt(3) approximately 5.19615... Simplifies because 27=9*3.

NUMBER LINE (√27 ≈ 5.1962)

√27

SQUARE WITH AREA = 27

Area = 27

√27

≈ 5.196

√27 ≈ 5.196

NEARBY PERFECT SQUARES

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

√64= 88² = 64

SQUARE ROOT LAWS

√27 × √27= 27

(√27)²= 27

√(27 × 4)= 2√27 ≈ 10.3923

√(27/4)= √27/2 ≈ 2.5981

√27 × √28≈ 27.4955

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 27: 27 = 3 x 3 x 3. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 3sqrt3. Pairs were extracted to simplify the radical.
3
Locate sqrt(27) between integers: 5 squared = 25 and 6 squared = 36. Since 25 < 27 < 36, sqrt(27) lies between 5 and 6.
4
Calculate decimal: sqrt(27) approximately 5.1961524227. Verify by squaring: (5.196152) squared approximately 27.0 = 27.

WORKED EXAMPLE

sqrt(27): not a perfect square. Factorisation: 27 = 3 x 3 x 3. Simplified: 3sqrt3. Decimal: sqrt(27) approximately 5.1961524227.

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 √28 √29 √30

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.