What is the square root of 5?

The square root of 5 is sqrt5. In decimal: sqrt(5) approximately 2.2360679775 This is irrational — the decimal never terminates or repeats. sqrt(5)=2.23606... appears in the golden ratio formula: phi=(1+sqrt(5))/2 approximately 1.618.

Is 5 a perfect square?

No. 5 is not a perfect square. 2 squared = 4 and 3 squared = 9. Since 5 falls between these, sqrt(5) is not an integer. Nearest perfect squares: 4 (= 2 squared) and 9 (= 3 squared).

How do you simplify sqrt(5)?

sqrt(5) simplifies to sqrt5. Method: prime factorisation of 5 = 5. Since no factor repeats, sqrt(5) cannot be simplified further.

What is sqrt(5) squared?

(sqrt(5)) squared = 5. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(5)) squared = 5 always.

What is the difference between square root and squaring?

Squaring 5: 5 squared = 25 (multiply 5 by itself). Square root of 5: sqrt(5) = sqrt5 approximately 2.2361. They are inverse operations: sqrt(5) squared = 5 and sqrt(5 squared) = 5 (for non-negative numbers).

Square Root of 5 — sqrt(5) = sqrt5

The square root of 5 is sqrt5. In decimal form, sqrt(5) approximately 2.236068 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√5 = ?

SQUARE ROOT OF 5

√5

≈ 2.2360679775

Irrational — cannot be expressed as a fraction

Exact form

√5

Decimal (4dp)

2.2361

Decimal (10dp)

2.2360679775

Is perfect sq?

√5 ²

5 ✓

Between

2 and 3

DECIMAL PRECISION

√5 ≈ 2.2360679775

STEP-BY-STEP

Prime factorisation: 5 = 5

Simplified radical form: √5

2² = 4 < 5 < 9 = 3² → lies between 2 and 3

√5 ≈ 2.2360679775...

FUN FACT

sqrt(5)=2.23606... appears in the golden ratio formula: phi=(1+sqrt(5))/2 approximately 1.618.

NUMBER LINE (√5 ≈ 2.2361)

√5

SQUARE WITH AREA = 5

Area = 5

√5

≈ 2.236

√5 ≈ 2.236

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

SQUARE ROOT LAWS

√5 × √5= 5

(√5)²= 5

√(5 × 4)= 2√5 ≈ 4.4721

√(5/4)= √5/2 ≈ 1.1180

√5 × √6≈ 5.4772

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HOW TO CALCULATE

1
Find the prime factorisation of 5: 5 = 5. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt5. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(5) between integers: 2 squared = 4 and 3 squared = 9. Since 4 < 5 < 9, sqrt(5) lies between 2 and 3.
4
Calculate decimal: sqrt(5) approximately 2.2360679775. Verify by squaring: (2.236068) squared approximately 5.0 = 5.

WORKED EXAMPLE

sqrt(5): not a perfect square. Factorisation: 5 = 5. Simplified: sqrt5. Decimal: sqrt(5) approximately 2.2360679775.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √6 √7 √8 √9 √10 √11 √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.