What is the square root of 8?

The square root of 8 is 2sqrt2. In decimal: sqrt(8) approximately 2.8284271247 This is irrational — the decimal never terminates or repeats. sqrt(8)=2*sqrt(2) approximately 2.82842... Simplifies because 8=4*2 and sqrt(4)=2. It is the diagonal of a square with side 2.

Is 8 a perfect square?

No. 8 is not a perfect square. 2 squared = 4 and 3 squared = 9. Since 8 falls between these, sqrt(8) is not an integer. Nearest perfect squares: 4 (= 2 squared) and 9 (= 3 squared).

How do you simplify sqrt(8)?

sqrt(8) simplifies to 2sqrt2. Method: prime factorisation of 8 = 2 x 2 x 2. Extract pairs of identical factors: result is 2sqrt2.

What is sqrt(8) squared?

(sqrt(8)) squared = 8. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(8)) squared = 8 always.

What is the difference between square root and squaring?

Squaring 8: 8 squared = 64 (multiply 8 by itself). Square root of 8: sqrt(8) = 2sqrt2 approximately 2.8284. They are inverse operations: sqrt(8) squared = 8 and sqrt(8 squared) = 8 (for non-negative numbers).

Square Root of 8 — sqrt(8) = 2sqrt2

The square root of 8 is 2sqrt2. In decimal form, sqrt(8) approximately 2.828427 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√8 = ?

SQUARE ROOT OF 8

2√2

≈ 2.8284271247

Irrational — cannot be expressed as a fraction

Exact form

2√2

Decimal (4dp)

2.8284

Decimal (10dp)

2.8284271247

Is perfect sq?

√8 ²

8 ✓

Between

2 and 3

DECIMAL PRECISION

√8 ≈ 2.8284271247

STEP-BY-STEP

Prime factorisation: 8 = 2 × 2 × 2

Simplified radical form: 2√2

2² = 4 < 8 < 9 = 3² → lies between 2 and 3

√8 ≈ 2.8284271247...

FUN FACT

sqrt(8)=2*sqrt(2) approximately 2.82842... Simplifies because 8=4*2 and sqrt(4)=2. It is the diagonal of a square with side 2.

NUMBER LINE (√8 ≈ 2.8284)

√8

SQUARE WITH AREA = 8

Area = 8

√8

≈ 2.828

√8 ≈ 2.828

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

SQUARE ROOT LAWS

√8 × √8= 8

(√8)²= 8

√(8 × 4)= 2√8 ≈ 5.6569

√(8/4)= √8/2 ≈ 1.4142

√8 × √9≈ 8.4853

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HOW TO CALCULATE

1
Find the prime factorisation of 8: 8 = 2 x 2 x 2. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 2sqrt2. Pairs were extracted to simplify the radical.
3
Locate sqrt(8) between integers: 2 squared = 4 and 3 squared = 9. Since 4 < 8 < 9, sqrt(8) lies between 2 and 3.
4
Calculate decimal: sqrt(8) approximately 2.8284271247. Verify by squaring: (2.828427) squared approximately 8.0 = 8.

WORKED EXAMPLE

sqrt(8): not a perfect square. Factorisation: 8 = 2 x 2 x 2. Simplified: 2sqrt2. Decimal: sqrt(8) approximately 2.8284271247.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √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.