What is the square root of 26?

The square root of 26 is sqrt26. In decimal: sqrt(26) approximately 5.0990195136 This is irrational — the decimal never terminates or repeats. sqrt(26)=5.09901...=sqrt(2)*sqrt(13). Has no repeated factors.

Is 26 a perfect square?

No. 26 is not a perfect square. 5 squared = 25 and 6 squared = 36. Since 26 falls between these, sqrt(26) is not an integer. Nearest perfect squares: 25 (= 5 squared) and 36 (= 6 squared).

How do you simplify sqrt(26)?

sqrt(26) simplifies to sqrt26. Method: prime factorisation of 26 = 2 x 13. Since no factor repeats, sqrt(26) cannot be simplified further.

What is sqrt(26) squared?

(sqrt(26)) squared = 26. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(26)) squared = 26 always.

What is the difference between square root and squaring?

Squaring 26: 26 squared = 676 (multiply 26 by itself). Square root of 26: sqrt(26) = sqrt26 approximately 5.0990. They are inverse operations: sqrt(26) squared = 26 and sqrt(26 squared) = 26 (for non-negative numbers).

Square Root of 26 — sqrt(26) = sqrt26

The square root of 26 is sqrt26. In decimal form, sqrt(26) approximately 5.09902 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√26 = ?

SQUARE ROOT OF 26

√26

≈ 5.0990195136

Irrational — cannot be expressed as a fraction

Exact form

√26

Decimal (4dp)

5.0990

Decimal (10dp)

5.0990195136

Is perfect sq?

√26 ²

26 ✓

Between

5 and 6

DECIMAL PRECISION

√26 ≈ 5.0990195136

STEP-BY-STEP

Prime factorisation: 26 = 2 × 13

Simplified radical form: √26

5² = 25 < 26 < 36 = 6² → lies between 5 and 6

√26 ≈ 5.0990195136...

FUN FACT

sqrt(26)=5.09901...=sqrt(2)*sqrt(13). Has no repeated factors.

NUMBER LINE (√26 ≈ 5.0990)

√26

SQUARE WITH AREA = 26

Area = 26

√26

≈ 5.099

√26 ≈ 5.099

NEARBY PERFECT SQUARES

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

√64= 88² = 64

SQUARE ROOT LAWS

√26 × √26= 26

(√26)²= 26

√(26 × 4)= 2√26 ≈ 10.1980

√(26/4)= √26/2 ≈ 2.5495

√26 × √27≈ 26.4953

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 26: 26 = 2 x 13. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt26. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(26) between integers: 5 squared = 25 and 6 squared = 36. Since 25 < 26 < 36, sqrt(26) lies between 5 and 6.
4
Calculate decimal: sqrt(26) approximately 5.0990195136. Verify by squaring: (5.099020) squared approximately 26.0 = 26.

WORKED EXAMPLE

sqrt(26): not a perfect square. Factorisation: 26 = 2 x 13. Simplified: sqrt26. Decimal: sqrt(26) approximately 5.0990195136.

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 √24 √25 √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.