What is the square root of 3?

The square root of 3 is sqrt3. In decimal: sqrt(3) approximately 1.7320508076 This is irrational — the decimal never terminates or repeats. sqrt(3)=1.73205... appears in equilateral triangle geometry: the height of an equilateral triangle with side 2 is exactly sqrt(3).

Is 3 a perfect square?

No. 3 is not a perfect square. 1 squared = 1 and 2 squared = 4. Since 3 falls between these, sqrt(3) is not an integer. Nearest perfect squares: 1 (= 1 squared) and 4 (= 2 squared).

How do you simplify sqrt(3)?

sqrt(3) simplifies to sqrt3. Method: prime factorisation of 3 = 3. Since no factor repeats, sqrt(3) cannot be simplified further.

What is sqrt(3) squared?

(sqrt(3)) squared = 3. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(3)) squared = 3 always.

What is the difference between square root and squaring?

Squaring 3: 3 squared = 9 (multiply 3 by itself). Square root of 3: sqrt(3) = sqrt3 approximately 1.7321. They are inverse operations: sqrt(3) squared = 3 and sqrt(3 squared) = 3 (for non-negative numbers).

Square Root of 3 — sqrt(3) = sqrt3

The square root of 3 is sqrt3. In decimal form, sqrt(3) approximately 1.732051 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√3 = ?

SQUARE ROOT OF 3

√3

≈ 1.7320508076

Irrational — cannot be expressed as a fraction

Exact form

√3

Decimal (4dp)

1.7321

Decimal (10dp)

1.7320508076

Is perfect sq?

√3 ²

3 ✓

Between

1 and 2

DECIMAL PRECISION

√3 ≈ 1.7320508076

STEP-BY-STEP

Prime factorisation: 3 = 3

Simplified radical form: √3

1² = 1 < 3 < 4 = 2² → lies between 1 and 2

√3 ≈ 1.7320508076...

FUN FACT

sqrt(3)=1.73205... appears in equilateral triangle geometry: the height of an equilateral triangle with side 2 is exactly sqrt(3).

NUMBER LINE (√3 ≈ 1.7321)

√3

SQUARE WITH AREA = 3

Area = 3

√3

≈ 1.732

√3 ≈ 1.732

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

SQUARE ROOT LAWS

√3 × √3= 3

(√3)²= 3

√(3 × 4)= 2√3 ≈ 3.4641

√(3/4)= √3/2 ≈ 0.8660

√3 × √4≈ 3.4641

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HOW TO CALCULATE

1
Find the prime factorisation of 3: 3 = 3. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt3. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(3) between integers: 1 squared = 1 and 2 squared = 4. Since 1 < 3 < 4, sqrt(3) lies between 1 and 2.
4
Calculate decimal: sqrt(3) approximately 1.7320508076. Verify by squaring: (1.732051) squared approximately 3.0 = 3.

WORKED EXAMPLE

sqrt(3): not a perfect square. Factorisation: 3 = 3. Simplified: sqrt3. Decimal: sqrt(3) approximately 1.7320508076.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √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 √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.