What is the square root of 13?

The square root of 13 is sqrt13. In decimal: sqrt(13) approximately 3.6055512755 This is irrational — the decimal never terminates or repeats. sqrt(13)=3.60555... is irrational. 13 is part of the (5,12,13) Pythagorean triple.

Is 13 a perfect square?

No. 13 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 13 falls between these, sqrt(13) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(13)?

sqrt(13) simplifies to sqrt13. Method: prime factorisation of 13 = 13. Since no factor repeats, sqrt(13) cannot be simplified further.

What is sqrt(13) squared?

(sqrt(13)) squared = 13. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(13)) squared = 13 always.

What is the difference between square root and squaring?

Squaring 13: 13 squared = 169 (multiply 13 by itself). Square root of 13: sqrt(13) = sqrt13 approximately 3.6056. They are inverse operations: sqrt(13) squared = 13 and sqrt(13 squared) = 13 (for non-negative numbers).

Square Root of 13 — sqrt(13) = sqrt13

The square root of 13 is sqrt13. In decimal form, sqrt(13) approximately 3.605551 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√13 = ?

SQUARE ROOT OF 13

√13

≈ 3.6055512755

Irrational — cannot be expressed as a fraction

Exact form

√13

Decimal (4dp)

3.6056

Decimal (10dp)

3.6055512755

Is perfect sq?

√13 ²

13 ✓

Between

3 and 4

DECIMAL PRECISION

√13 ≈ 3.6055512755

STEP-BY-STEP

Prime factorisation: 13 = 13

Simplified radical form: √13

3² = 9 < 13 < 16 = 4² → lies between 3 and 4

√13 ≈ 3.6055512755...

FUN FACT

sqrt(13)=3.60555... is irrational. 13 is part of the (5,12,13) Pythagorean triple.

NUMBER LINE (√13 ≈ 3.6056)

√13

SQUARE WITH AREA = 13

Area = 13

√13

≈ 3.606

√13 ≈ 3.606

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√13 × √13= 13

(√13)²= 13

√(13 × 4)= 2√13 ≈ 7.2111

√(13/4)= √13/2 ≈ 1.8028

√13 × √14≈ 13.4907

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HOW TO CALCULATE

1
Find the prime factorisation of 13: 13 = 13. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt13. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(13) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 13 < 16, sqrt(13) lies between 3 and 4.
4
Calculate decimal: sqrt(13) approximately 3.6055512755. Verify by squaring: (3.605551) squared approximately 13.0 = 13.

WORKED EXAMPLE

sqrt(13): not a perfect square. Factorisation: 13 = 13. Simplified: sqrt13. Decimal: sqrt(13) approximately 3.6055512755.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √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.