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?

No

√8 ²

8 ✓

Between

2 and 3

DECIMAL PRECISION

√8 ≈ 2.8284271247

STEP-BY-STEP

1

Prime factorisation: 8 = 2 × 2 × 2

2

Simplified radical form: 2√2

3

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

4

√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)

2

3

√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
Created with❤️byeaglecalculator.com

HOW TO CALCULATE

  1. 1

    Find the prime factorisation of 8: 8 = 2 x 2 x 2. Check for repeated prime factors.

  2. 2

    Simplify: pull out any pairs of identical prime factors. Result: 2sqrt2. Pairs were extracted to simplify the radical.

  3. 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. 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.