Square Root of 7 — sqrt(7) = sqrt7

The square root of 7 is sqrt7. In decimal form, sqrt(7) approximately 2.645751 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√7 = ?

SQUARE ROOT OF 7

√7

≈ 2.6457513111

Irrational — cannot be expressed as a fraction

Exact form

√7

Decimal (4dp)

2.6458

Decimal (10dp)

2.6457513111

Is perfect sq?

No

√7 ²

7 ✓

Between

2 and 3

DECIMAL PRECISION

√7 ≈ 2.6457513111

STEP-BY-STEP

1

Prime factorisation: 7 = 7

2

Simplified radical form: √7

3

2² = 4 < 7 < 9 = 3² → lies between 2 and 3

4

√7 ≈ 2.6457513111...

FUN FACT

sqrt(7)=2.64575... is irrational. 7 is prime so sqrt(7) cannot be simplified.

NUMBER LINE (√7 ≈ 2.6458)

2

3

√7

SQUARE WITH AREA = 7

Area = 7

√7

≈ 2.646

√7 ≈ 2.646

NEARBY PERFECT SQUARES

√1= 11² = 1
√4= 22² = 4
√9= 33² = 9
√16= 44² = 16
√25= 55² = 25

SQUARE ROOT LAWS

√7 × √7= 7
(√7)²= 7
√(7 × 4)= 2√7 ≈ 5.2915
√(7/4)= √7/2 ≈ 1.3229
√7 × √8≈ 7.4833
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HOW TO CALCULATE

  1. 1

    Find the prime factorisation of 7: 7 = 7. Check for repeated prime factors.

  2. 2

    Simplify: pull out any pairs of identical prime factors. Result: sqrt7. Since no factor repeats, it cannot be simplified further.

  3. 3

    Locate sqrt(7) between integers: 2 squared = 4 and 3 squared = 9. Since 4 < 7 < 9, sqrt(7) lies between 2 and 3.

  4. 4

    Calculate decimal: sqrt(7) approximately 2.6457513111. Verify by squaring: (2.645751) squared approximately 7.0 = 7.

WORKED EXAMPLE

sqrt(7): not a perfect square. Factorisation: 7 = 7. Simplified: sqrt7. Decimal: sqrt(7) approximately 2.6457513111.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1√2√3√4√5√6√8√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.