What is the square root of 14?

The square root of 14 is sqrt14. In decimal: sqrt(14) approximately 3.7416573868 This is irrational — the decimal never terminates or repeats. sqrt(14)=3.74165...=sqrt(2)*sqrt(7). Has no repeated prime factors so stays as sqrt(14).

Is 14 a perfect square?

No. 14 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 14 falls between these, sqrt(14) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(14)?

sqrt(14) simplifies to sqrt14. Method: prime factorisation of 14 = 2 x 7. Since no factor repeats, sqrt(14) cannot be simplified further.

What is sqrt(14) squared?

(sqrt(14)) squared = 14. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(14)) squared = 14 always.

What is the difference between square root and squaring?

Squaring 14: 14 squared = 196 (multiply 14 by itself). Square root of 14: sqrt(14) = sqrt14 approximately 3.7417. They are inverse operations: sqrt(14) squared = 14 and sqrt(14 squared) = 14 (for non-negative numbers).

Square Root of 14 — sqrt(14) = sqrt14

The square root of 14 is sqrt14. In decimal form, sqrt(14) approximately 3.741657 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√14 = ?

SQUARE ROOT OF 14

√14

≈ 3.7416573868

Irrational — cannot be expressed as a fraction

Exact form

√14

Decimal (4dp)

3.7417

Decimal (10dp)

3.7416573868

Is perfect sq?

√14 ²

14 ✓

Between

3 and 4

DECIMAL PRECISION

√14 ≈ 3.7416573868

STEP-BY-STEP

Prime factorisation: 14 = 2 × 7

Simplified radical form: √14

3² = 9 < 14 < 16 = 4² → lies between 3 and 4

√14 ≈ 3.7416573868...

FUN FACT

sqrt(14)=3.74165...=sqrt(2)*sqrt(7). Has no repeated prime factors so stays as sqrt(14).

NUMBER LINE (√14 ≈ 3.7417)

√14

SQUARE WITH AREA = 14

Area = 14

√14

≈ 3.742

√14 ≈ 3.742

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√14 × √14= 14

(√14)²= 14

√(14 × 4)= 2√14 ≈ 7.4833

√(14/4)= √14/2 ≈ 1.8708

√14 × √15≈ 14.4914

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HOW TO CALCULATE

1
Find the prime factorisation of 14: 14 = 2 x 7. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt14. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(14) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 14 < 16, sqrt(14) lies between 3 and 4.
4
Calculate decimal: sqrt(14) approximately 3.7416573868. Verify by squaring: (3.741657) squared approximately 14.0 = 14.

WORKED EXAMPLE

sqrt(14): not a perfect square. Factorisation: 14 = 2 x 7. Simplified: sqrt14. Decimal: sqrt(14) approximately 3.7416573868.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √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.