What is the square root of 20?

The square root of 20 is 2sqrt5. In decimal: sqrt(20) approximately 4.4721359550 This is irrational — the decimal never terminates or repeats. sqrt(20)=2*sqrt(5) approximately 4.47213... Simplifies because 20=4*5.

Is 20 a perfect square?

No. 20 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 20 falls between these, sqrt(20) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(20)?

sqrt(20) simplifies to 2sqrt5. Method: prime factorisation of 20 = 2 x 2 x 5. Extract pairs of identical factors: result is 2sqrt5.

What is sqrt(20) squared?

(sqrt(20)) squared = 20. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(20)) squared = 20 always.

What is the difference between square root and squaring?

Squaring 20: 20 squared = 400 (multiply 20 by itself). Square root of 20: sqrt(20) = 2sqrt5 approximately 4.4721. They are inverse operations: sqrt(20) squared = 20 and sqrt(20 squared) = 20 (for non-negative numbers).

Square Root of 20 — sqrt(20) = 2sqrt5

The square root of 20 is 2sqrt5. In decimal form, sqrt(20) approximately 4.472136 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√20 = ?

SQUARE ROOT OF 20

2√5

≈ 4.4721359550

Irrational — cannot be expressed as a fraction

Exact form

2√5

Decimal (4dp)

4.4721

Decimal (10dp)

4.4721359550

Is perfect sq?

√20 ²

20 ✓

Between

4 and 5

DECIMAL PRECISION

√20 ≈ 4.4721359550

STEP-BY-STEP

Prime factorisation: 20 = 2 × 2 × 5

Simplified radical form: 2√5

4² = 16 < 20 < 25 = 5² → lies between 4 and 5

√20 ≈ 4.4721359550...

FUN FACT

sqrt(20)=2*sqrt(5) approximately 4.47213... Simplifies because 20=4*5.

NUMBER LINE (√20 ≈ 4.4721)

√20

SQUARE WITH AREA = 20

Area = 20

√20

≈ 4.472

√20 ≈ 4.472

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√20 × √20= 20

(√20)²= 20

√(20 × 4)= 2√20 ≈ 8.9443

√(20/4)= √20/2 ≈ 2.2361

√20 × √21≈ 20.4939

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HOW TO CALCULATE

1
Find the prime factorisation of 20: 20 = 2 x 2 x 5. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 2sqrt5. Pairs were extracted to simplify the radical.
3
Locate sqrt(20) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 20 < 25, sqrt(20) lies between 4 and 5.
4
Calculate decimal: sqrt(20) approximately 4.4721359550. Verify by squaring: (4.472136) squared approximately 20.0 = 20.

WORKED EXAMPLE

sqrt(20): not a perfect square. Factorisation: 20 = 2 x 2 x 5. Simplified: 2sqrt5. Decimal: sqrt(20) approximately 4.4721359550.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √17 √18 √19 √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.