What is the square root of 15?

The square root of 15 is sqrt15. In decimal: sqrt(15) approximately 3.8729833462 This is irrational — the decimal never terminates or repeats. sqrt(15)=3.87298...=sqrt(3)*sqrt(5). Has no repeated prime factors so stays as sqrt(15).

Is 15 a perfect square?

No. 15 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 15 falls between these, sqrt(15) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(15)?

sqrt(15) simplifies to sqrt15. Method: prime factorisation of 15 = 3 x 5. Since no factor repeats, sqrt(15) cannot be simplified further.

What is sqrt(15) squared?

(sqrt(15)) squared = 15. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(15)) squared = 15 always.

What is the difference between square root and squaring?

Squaring 15: 15 squared = 225 (multiply 15 by itself). Square root of 15: sqrt(15) = sqrt15 approximately 3.8730. They are inverse operations: sqrt(15) squared = 15 and sqrt(15 squared) = 15 (for non-negative numbers).

Square Root of 15 — sqrt(15) = sqrt15

The square root of 15 is sqrt15. In decimal form, sqrt(15) approximately 3.872983 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√15 = ?

SQUARE ROOT OF 15

√15

≈ 3.8729833462

Irrational — cannot be expressed as a fraction

Exact form

√15

Decimal (4dp)

3.8730

Decimal (10dp)

3.8729833462

Is perfect sq?

√15 ²

15 ✓

Between

3 and 4

DECIMAL PRECISION

√15 ≈ 3.8729833462

STEP-BY-STEP

Prime factorisation: 15 = 3 × 5

Simplified radical form: √15

3² = 9 < 15 < 16 = 4² → lies between 3 and 4

√15 ≈ 3.8729833462...

FUN FACT

sqrt(15)=3.87298...=sqrt(3)*sqrt(5). Has no repeated prime factors so stays as sqrt(15).

NUMBER LINE (√15 ≈ 3.8730)

√15

SQUARE WITH AREA = 15

Area = 15

√15

≈ 3.873

√15 ≈ 3.873

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√15 × √15= 15

(√15)²= 15

√(15 × 4)= 2√15 ≈ 7.7460

√(15/4)= √15/2 ≈ 1.9365

√15 × √16≈ 15.4919

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HOW TO CALCULATE

1
Find the prime factorisation of 15: 15 = 3 x 5. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt15. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(15) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 15 < 16, sqrt(15) lies between 3 and 4.
4
Calculate decimal: sqrt(15) approximately 3.8729833462. Verify by squaring: (3.872983) squared approximately 15.0 = 15.

WORKED EXAMPLE

sqrt(15): not a perfect square. Factorisation: 15 = 3 x 5. Simplified: sqrt15. Decimal: sqrt(15) approximately 3.8729833462.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √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.