What is the square root of 10?

The square root of 10 is sqrt10. In decimal: sqrt(10) approximately 3.1622776602 This is irrational — the decimal never terminates or repeats. sqrt(10)=3.16227... is close to pi (3.14159). This approximation was used in ancient mathematics.

Is 10 a perfect square?

No. 10 is not a perfect square. 3 squared = 9 and 4 squared = 16. Since 10 falls between these, sqrt(10) is not an integer. Nearest perfect squares: 9 (= 3 squared) and 16 (= 4 squared).

How do you simplify sqrt(10)?

sqrt(10) simplifies to sqrt10. Method: prime factorisation of 10 = 2 x 5. Since no factor repeats, sqrt(10) cannot be simplified further.

What is sqrt(10) squared?

(sqrt(10)) squared = 10. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(10)) squared = 10 always.

What is the difference between square root and squaring?

Squaring 10: 10 squared = 100 (multiply 10 by itself). Square root of 10: sqrt(10) = sqrt10 approximately 3.1623. They are inverse operations: sqrt(10) squared = 10 and sqrt(10 squared) = 10 (for non-negative numbers).

Square Root of 10 — sqrt(10) = sqrt10

The square root of 10 is sqrt10. In decimal form, sqrt(10) approximately 3.162278 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√10 = ?

SQUARE ROOT OF 10

√10

≈ 3.1622776602

Irrational — cannot be expressed as a fraction

Exact form

√10

Decimal (4dp)

3.1623

Decimal (10dp)

3.1622776602

Is perfect sq?

√10 ²

10 ✓

Between

3 and 4

DECIMAL PRECISION

√10 ≈ 3.1622776602

STEP-BY-STEP

Prime factorisation: 10 = 2 × 5

Simplified radical form: √10

3² = 9 < 10 < 16 = 4² → lies between 3 and 4

√10 ≈ 3.1622776602...

FUN FACT

sqrt(10)=3.16227... is close to pi (3.14159). This approximation was used in ancient mathematics.

NUMBER LINE (√10 ≈ 3.1623)

√10

SQUARE WITH AREA = 10

Area = 10

√10

≈ 3.162

√10 ≈ 3.162

NEARBY PERFECT SQUARES

√1= 11² = 1

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

SQUARE ROOT LAWS

√10 × √10= 10

(√10)²= 10

√(10 × 4)= 2√10 ≈ 6.3246

√(10/4)= √10/2 ≈ 1.5811

√10 × √11≈ 10.4881

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 10: 10 = 2 x 5. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt10. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(10) between integers: 3 squared = 9 and 4 squared = 16. Since 9 < 10 < 16, sqrt(10) lies between 3 and 4.
4
Calculate decimal: sqrt(10) approximately 3.1622776602. Verify by squaring: (3.162278) squared approximately 10.0 = 10.

WORKED EXAMPLE

sqrt(10): not a perfect square. Factorisation: 10 = 2 x 5. Simplified: sqrt10. Decimal: sqrt(10) approximately 3.1622776602.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √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)

RELATED CALCULATORS

Cube Root of 2

Calculate instantly →

Square Root of 22

Calculate instantly →

6 Times Table

Calculate instantly →

Cube Root of 29

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 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.