What is the square root of 12?

The square root of 12 is 2sqrt3. In decimal: sqrt(12) approximately 3.4641016151 This is irrational — the decimal never terminates or repeats. sqrt(12)=2*sqrt(3) approximately 3.46410... Simplifies because 12=4*3.

Is 12 a perfect square?

No. 12 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 12 falls between these, sqrt(12) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(12)?

sqrt(12) simplifies to 2sqrt3. Method: prime factorisation of 12 = 2 x 2 x 3. Extract pairs of identical factors: result is 2sqrt3.

What is sqrt(12) squared?

(sqrt(12)) squared = 12. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(12)) squared = 12 always.

What is the difference between square root and squaring?

Squaring 12: 12 squared = 144 (multiply 12 by itself). Square root of 12: sqrt(12) = 2sqrt3 approximately 3.4641. They are inverse operations: sqrt(12) squared = 12 and sqrt(12 squared) = 12 (for non-negative numbers).

Square Root of 12 — sqrt(12) = 2sqrt3

The square root of 12 is 2sqrt3. In decimal form, sqrt(12) approximately 3.464102 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√12 = ?

SQUARE ROOT OF 12

2√3

≈ 3.4641016151

Irrational — cannot be expressed as a fraction

Exact form

2√3

Decimal (4dp)

3.4641

Decimal (10dp)

3.4641016151

Is perfect sq?

√12 ²

12 ✓

Between

3 and 4

DECIMAL PRECISION

√12 ≈ 3.4641016151

STEP-BY-STEP

Prime factorisation: 12 = 2 × 2 × 3

Simplified radical form: 2√3

3² = 9 < 12 < 16 = 4² → lies between 3 and 4

√12 ≈ 3.4641016151...

FUN FACT

sqrt(12)=2*sqrt(3) approximately 3.46410... Simplifies because 12=4*3.

NUMBER LINE (√12 ≈ 3.4641)

√12

SQUARE WITH AREA = 12

Area = 12

√12

≈ 3.464

√12 ≈ 3.464

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√12 × √12= 12

(√12)²= 12

√(12 × 4)= 2√12 ≈ 6.9282

√(12/4)= √12/2 ≈ 1.7321

√12 × √13≈ 12.4900

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 12: 12 = 2 x 2 x 3. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 2sqrt3. Pairs were extracted to simplify the radical.
3
Locate sqrt(12) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 12 < 16, sqrt(12) lies between 3 and 4.
4
Calculate decimal: sqrt(12) approximately 3.4641016151. Verify by squaring: (3.464102) squared approximately 12.0 = 12.

WORKED EXAMPLE

sqrt(12): not a perfect square. Factorisation: 12 = 2 x 2 x 3. Simplified: 2sqrt3. Decimal: sqrt(12) approximately 3.4641016151.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √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.