What is the square root of 11?

The square root of 11 is sqrt11. In decimal: sqrt(11) approximately 3.3166247904 This is irrational — the decimal never terminates or repeats. sqrt(11)=3.31662... is irrational. 11 is prime so sqrt(11) cannot be simplified.

Is 11 a perfect square?

No. 11 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 11 falls between these, sqrt(11) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(11)?

sqrt(11) simplifies to sqrt11. Method: prime factorisation of 11 = 11. Since no factor repeats, sqrt(11) cannot be simplified further.

What is sqrt(11) squared?

(sqrt(11)) squared = 11. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(11)) squared = 11 always.

What is the difference between square root and squaring?

Squaring 11: 11 squared = 121 (multiply 11 by itself). Square root of 11: sqrt(11) = sqrt11 approximately 3.3166. They are inverse operations: sqrt(11) squared = 11 and sqrt(11 squared) = 11 (for non-negative numbers).

Square Root of 11 — sqrt(11) = sqrt11

The square root of 11 is sqrt11. In decimal form, sqrt(11) approximately 3.316625 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√11 = ?

SQUARE ROOT OF 11

√11

≈ 3.3166247904

Irrational — cannot be expressed as a fraction

Exact form

√11

Decimal (4dp)

3.3166

Decimal (10dp)

3.3166247904

Is perfect sq?

√11 ²

11 ✓

Between

3 and 4

DECIMAL PRECISION

√11 ≈ 3.3166247904

STEP-BY-STEP

Prime factorisation: 11 = 11

Simplified radical form: √11

3² = 9 < 11 < 16 = 4² → lies between 3 and 4

√11 ≈ 3.3166247904...

FUN FACT

sqrt(11)=3.31662... is irrational. 11 is prime so sqrt(11) cannot be simplified.

NUMBER LINE (√11 ≈ 3.3166)

√11

SQUARE WITH AREA = 11

Area = 11

√11

≈ 3.317

√11 ≈ 3.317

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√11 × √11= 11

(√11)²= 11

√(11 × 4)= 2√11 ≈ 6.6332

√(11/4)= √11/2 ≈ 1.6583

√11 × √12≈ 11.4891

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 11: 11 = 11. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt11. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(11) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 11 < 16, sqrt(11) lies between 3 and 4.
4
Calculate decimal: sqrt(11) approximately 3.3166247904. Verify by squaring: (3.316625) squared approximately 11.0 = 11.

WORKED EXAMPLE

sqrt(11): not a perfect square. Factorisation: 11 = 11. Simplified: sqrt11. Decimal: sqrt(11) approximately 3.3166247904.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √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.