What is the square root of 23?

The square root of 23 is sqrt23. In decimal: sqrt(23) approximately 4.7958315233 This is irrational — the decimal never terminates or repeats. sqrt(23)=4.79583... is irrational. 23 is prime.

Is 23 a perfect square?

No. 23 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 23 falls between these, sqrt(23) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(23)?

sqrt(23) simplifies to sqrt23. Method: prime factorisation of 23 = 23. Since no factor repeats, sqrt(23) cannot be simplified further.

What is sqrt(23) squared?

(sqrt(23)) squared = 23. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(23)) squared = 23 always.

What is the difference between square root and squaring?

Squaring 23: 23 squared = 529 (multiply 23 by itself). Square root of 23: sqrt(23) = sqrt23 approximately 4.7958. They are inverse operations: sqrt(23) squared = 23 and sqrt(23 squared) = 23 (for non-negative numbers).

Square Root of 23 — sqrt(23) = sqrt23

The square root of 23 is sqrt23. In decimal form, sqrt(23) approximately 4.795832 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√23 = ?

SQUARE ROOT OF 23

√23

≈ 4.7958315233

Irrational — cannot be expressed as a fraction

Exact form

√23

Decimal (4dp)

4.7958

Decimal (10dp)

4.7958315233

Is perfect sq?

√23 ²

23 ✓

Between

4 and 5

DECIMAL PRECISION

√23 ≈ 4.7958315233

STEP-BY-STEP

Prime factorisation: 23 = 23

Simplified radical form: √23

4² = 16 < 23 < 25 = 5² → lies between 4 and 5

√23 ≈ 4.7958315233...

FUN FACT

sqrt(23)=4.79583... is irrational. 23 is prime.

NUMBER LINE (√23 ≈ 4.7958)

√23

SQUARE WITH AREA = 23

Area = 23

√23

≈ 4.796

√23 ≈ 4.796

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√23 × √23= 23

(√23)²= 23

√(23 × 4)= 2√23 ≈ 9.5917

√(23/4)= √23/2 ≈ 2.3979

√23 × √24≈ 23.4947

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 23: 23 = 23. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt23. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(23) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 23 < 25, sqrt(23) lies between 4 and 5.
4
Calculate decimal: sqrt(23) approximately 4.7958315233. Verify by squaring: (4.795832) squared approximately 23.0 = 23.

WORKED EXAMPLE

sqrt(23): not a perfect square. Factorisation: 23 = 23. Simplified: sqrt23. Decimal: sqrt(23) approximately 4.7958315233.

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 √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.