What is the square root of 18?

The square root of 18 is 3sqrt2. In decimal: sqrt(18) approximately 4.2426406871 This is irrational — the decimal never terminates or repeats. sqrt(18)=3*sqrt(2) approximately 4.24264... Simplifies because 18=9*2 and sqrt(9)=3.

Is 18 a perfect square?

No. 18 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 18 falls between these, sqrt(18) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(18)?

sqrt(18) simplifies to 3sqrt2. Method: prime factorisation of 18 = 2 x 3 x 3. Extract pairs of identical factors: result is 3sqrt2.

What is sqrt(18) squared?

(sqrt(18)) squared = 18. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(18)) squared = 18 always.

What is the difference between square root and squaring?

Squaring 18: 18 squared = 324 (multiply 18 by itself). Square root of 18: sqrt(18) = 3sqrt2 approximately 4.2426. They are inverse operations: sqrt(18) squared = 18 and sqrt(18 squared) = 18 (for non-negative numbers).

Square Root of 18 — sqrt(18) = 3sqrt2

The square root of 18 is 3sqrt2. In decimal form, sqrt(18) approximately 4.242641 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√18 = ?

SQUARE ROOT OF 18

3√2

≈ 4.2426406871

Irrational — cannot be expressed as a fraction

Exact form

3√2

Decimal (4dp)

4.2426

Decimal (10dp)

4.2426406871

Is perfect sq?

√18 ²

18 ✓

Between

4 and 5

DECIMAL PRECISION

√18 ≈ 4.2426406871

STEP-BY-STEP

Prime factorisation: 18 = 2 × 3 × 3

Simplified radical form: 3√2

4² = 16 < 18 < 25 = 5² → lies between 4 and 5

√18 ≈ 4.2426406871...

FUN FACT

sqrt(18)=3*sqrt(2) approximately 4.24264... Simplifies because 18=9*2 and sqrt(9)=3.

NUMBER LINE (√18 ≈ 4.2426)

√18

SQUARE WITH AREA = 18

Area = 18

√18

≈ 4.243

√18 ≈ 4.243

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√18 × √18= 18

(√18)²= 18

√(18 × 4)= 2√18 ≈ 8.4853

√(18/4)= √18/2 ≈ 2.1213

√18 × √19≈ 18.4932

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 18: 18 = 2 x 3 x 3. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: 3sqrt2. Pairs were extracted to simplify the radical.
3
Locate sqrt(18) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 18 < 25, sqrt(18) lies between 4 and 5.
4
Calculate decimal: sqrt(18) approximately 4.2426406871. Verify by squaring: (4.242641) squared approximately 18.0 = 18.

WORKED EXAMPLE

sqrt(18): not a perfect square. Factorisation: 18 = 2 x 3 x 3. Simplified: 3sqrt2. Decimal: sqrt(18) approximately 4.2426406871.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √17 √19 √20 √21 √22 √23 √24 √25 √26 √27 √28 √29 √30

Bold bordered = perfect squares (exact integer result)

RELATED CALCULATORS

Square Root of 19

Calculate instantly →

8 to the Power of 3

Calculate instantly →

10 to the Power of 5

Calculate instantly →

7 to the Power of 6

Calculate instantly →

MORE ALGEBRA CALCULATORS

23 Times Table

Calculate instantly →

24 Times Table

Calculate instantly →

Quadratic Equation Solver

Calculate instantly →

Logarithm Calculator

Calculate instantly →

Fraction Calculator

Calculate instantly →

Fraction Simplifier

Calculate instantly →

Linear Equation Solver

Calculate instantly →

25 Times Table

Calculate instantly →

26 Times Table

Calculate instantly →

27 Times Table

Calculate instantly →

Simultaneous Equations Solver (2×2)

Calculate instantly →

28 Times Table

Calculate instantly →

Exponent Calculator

Calculate instantly →

29 Times Table

Calculate instantly →

30 Times Table

Calculate instantly →

Times Tables Mega Calculator

Calculate instantly →

Square Root of 10

Calculate instantly →

Square Root of 1

Calculate instantly →

Square Root Mega

Calculate instantly →

Square Root of 22

Calculate instantly →

Was this calculator helpful?

Last updated: April 28, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.