What is the square root of 24?

The square root of 24 is 2sqrt6. In decimal: sqrt(24) approximately 4.8989794856 This is irrational — the decimal never terminates or repeats. sqrt(24)=2*sqrt(6) approximately 4.89897... Simplifies because 24=4*6.

Is 24 a perfect square?

No. 24 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 24 falls between these, sqrt(24) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(24)?

sqrt(24) simplifies to 2sqrt6. Method: prime factorisation of 24 = 2 x 2 x 2 x 3. Extract pairs of identical factors: result is 2sqrt6.

What is sqrt(24) squared?

(sqrt(24)) squared = 24. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(24)) squared = 24 always.

What is the difference between square root and squaring?

Squaring 24: 24 squared = 576 (multiply 24 by itself). Square root of 24: sqrt(24) = 2sqrt6 approximately 4.8990. They are inverse operations: sqrt(24) squared = 24 and sqrt(24 squared) = 24 (for non-negative numbers).

Square Root of 24 — sqrt(24) = 2sqrt6

The square root of 24 is 2sqrt6. In decimal form, sqrt(24) approximately 4.898979 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√24 = ?

SQUARE ROOT OF 24

2√6

≈ 4.8989794856

Irrational — cannot be expressed as a fraction

Exact form

2√6

Decimal (4dp)

4.8990

Decimal (10dp)

4.8989794856

Is perfect sq?

√24 ²

24 ✓

Between

4 and 5

DECIMAL PRECISION

√24 ≈ 4.8989794856

STEP-BY-STEP

Prime factorisation: 24 = 2 × 2 × 2 × 3

Simplified radical form: 2√6

4² = 16 < 24 < 25 = 5² → lies between 4 and 5

√24 ≈ 4.8989794856...

FUN FACT

sqrt(24)=2*sqrt(6) approximately 4.89897... Simplifies because 24=4*6.

NUMBER LINE (√24 ≈ 4.8990)

√24

SQUARE WITH AREA = 24

Area = 24

√24

≈ 4.899

√24 ≈ 4.899

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√24 × √24= 24

(√24)²= 24

√(24 × 4)= 2√24 ≈ 9.7980

√(24/4)= √24/2 ≈ 2.4495

√24 × √25≈ 24.4949

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HOW TO CALCULATE

1
Find the prime factorisation of 24: 24 = 2 x 2 x 2 x 3. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 2sqrt6. Pairs were extracted to simplify the radical.
3
Locate sqrt(24) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 24 < 25, sqrt(24) lies between 4 and 5.
4
Calculate decimal: sqrt(24) approximately 4.8989794856. Verify by squaring: (4.898979) squared approximately 24.0 = 24.

WORKED EXAMPLE

sqrt(24): not a perfect square. Factorisation: 24 = 2 x 2 x 2 x 3. Simplified: 2sqrt6. Decimal: sqrt(24) approximately 4.8989794856.

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 √21 √22 √23 √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.