What is the square root of 21?

The square root of 21 is sqrt21. In decimal: sqrt(21) approximately 4.5825756950 This is irrational — the decimal never terminates or repeats. sqrt(21)=4.58257...=sqrt(3)*sqrt(7). Has no repeated factors so stays as sqrt(21).

Is 21 a perfect square?

No. 21 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 21 falls between these, sqrt(21) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(21)?

sqrt(21) simplifies to sqrt21. Method: prime factorisation of 21 = 3 x 7. Since no factor repeats, sqrt(21) cannot be simplified further.

What is sqrt(21) squared?

(sqrt(21)) squared = 21. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(21)) squared = 21 always.

What is the difference between square root and squaring?

Squaring 21: 21 squared = 441 (multiply 21 by itself). Square root of 21: sqrt(21) = sqrt21 approximately 4.5826. They are inverse operations: sqrt(21) squared = 21 and sqrt(21 squared) = 21 (for non-negative numbers).

Square Root of 21 — sqrt(21) = sqrt21

The square root of 21 is sqrt21. In decimal form, sqrt(21) approximately 4.582576 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√21 = ?

SQUARE ROOT OF 21

√21

≈ 4.5825756950

Irrational — cannot be expressed as a fraction

Exact form

√21

Decimal (4dp)

4.5826

Decimal (10dp)

4.5825756950

Is perfect sq?

√21 ²

21 ✓

Between

4 and 5

DECIMAL PRECISION

√21 ≈ 4.5825756950

STEP-BY-STEP

Prime factorisation: 21 = 3 × 7

Simplified radical form: √21

4² = 16 < 21 < 25 = 5² → lies between 4 and 5

√21 ≈ 4.5825756950...

FUN FACT

sqrt(21)=4.58257...=sqrt(3)*sqrt(7). Has no repeated factors so stays as sqrt(21).

NUMBER LINE (√21 ≈ 4.5826)

√21

SQUARE WITH AREA = 21

Area = 21

√21

≈ 4.583

√21 ≈ 4.583

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√21 × √21= 21

(√21)²= 21

√(21 × 4)= 2√21 ≈ 9.1652

√(21/4)= √21/2 ≈ 2.2913

√21 × √22≈ 21.4942

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HOW TO CALCULATE

1
Find the prime factorisation of 21: 21 = 3 x 7. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt21. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(21) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 21 < 25, sqrt(21) lies between 4 and 5.
4
Calculate decimal: sqrt(21) approximately 4.5825756950. Verify by squaring: (4.582576) squared approximately 21.0 = 21.

WORKED EXAMPLE

sqrt(21): not a perfect square. Factorisation: 21 = 3 x 7. Simplified: sqrt21. Decimal: sqrt(21) approximately 4.5825756950.

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 √20 √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.