What is the square root of 2?

The square root of 2 is sqrt2. In decimal: sqrt(2) approximately 1.4142135624 This is irrational — the decimal never terminates or repeats. sqrt(2)=1.41421... was the first number proven irrational by the ancient Greeks. Legend says Hippasus was drowned for revealing this to the Pythagoreans.

Is 2 a perfect square?

No. 2 is not a perfect square. 1 squared = 1 and 2 squared = 4. Since 2 falls between these, sqrt(2) is not an integer. Nearest perfect squares: 1 (= 1 squared) and 4 (= 2 squared).

How do you simplify sqrt(2)?

sqrt(2) simplifies to sqrt2. Method: prime factorisation of 2 = 2. Since no factor repeats, sqrt(2) cannot be simplified further.

What is sqrt(2) squared?

(sqrt(2)) squared = 2. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(2)) squared = 2 always.

What is the difference between square root and squaring?

Squaring 2: 2 squared = 4 (multiply 2 by itself). Square root of 2: sqrt(2) = sqrt2 approximately 1.4142. They are inverse operations: sqrt(2) squared = 2 and sqrt(2 squared) = 2 (for non-negative numbers).

Square Root of 2 — sqrt(2) = sqrt2

The square root of 2 is sqrt2. In decimal form, sqrt(2) approximately 1.414214 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√2 = ?

SQUARE ROOT OF 2

√2

≈ 1.4142135624

Irrational — cannot be expressed as a fraction

Exact form

√2

Decimal (4dp)

1.4142

Decimal (10dp)

1.4142135624

Is perfect sq?

√2 ²

2 ✓

Between

1 and 2

DECIMAL PRECISION

√2 ≈ 1.4142135624

STEP-BY-STEP

Prime factorisation: 2 = 2

Simplified radical form: √2

1² = 1 < 2 < 4 = 2² → lies between 1 and 2

√2 ≈ 1.4142135624...

FUN FACT

sqrt(2)=1.41421... was the first number proven irrational by the ancient Greeks. Legend says Hippasus was drowned for revealing this to the Pythagoreans.

NUMBER LINE (√2 ≈ 1.4142)

√2

SQUARE WITH AREA = 2

Area = 2

√2

≈ 1.414

√2 ≈ 1.414

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

SQUARE ROOT LAWS

√2 × √2= 2

(√2)²= 2

√(2 × 4)= 2√2 ≈ 2.8284

√(2/4)= √2/2 ≈ 0.7071

√2 × √3≈ 2.4495

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 2: 2 = 2. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt2. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(2) between integers: 1 squared = 1 and 2 squared = 4. Since 1 < 2 < 4, sqrt(2) lies between 1 and 2.
4
Calculate decimal: sqrt(2) approximately 1.4142135624. Verify by squaring: (1.414214) squared approximately 2.0 = 2.

WORKED EXAMPLE

sqrt(2): not a perfect square. Factorisation: 2 = 2. Simplified: sqrt2. Decimal: sqrt(2) approximately 1.4142135624.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √3 √4 √5 √6 √7 √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.