A day full of math games & activities. Find one near you.

Square Root of 6

The square root of 6 is expressed as √6 in the radical form and as (6)^½ or (6)^0.5 in the exponent form. The square root of 6 rounded up to 7 decimal places is 2.4494897. It is the positive solution of the equation x² = 6.

Square Root of 6: 2.449489742783178
Square Root of 6 in exponential form: (6)^½ or (6)^0.5
Square Root of 6 in radical form: √6

1.	What Is the Square Root of 6?
2.	Is the Square Root of 6 Rational or Irrational?
3.	How to Find the Square Root of 6?
4.	Important Notes
5.	FAQs on Square Root of 6

What Is the Square Root of 6?

The square root of a number n is written as √n. The square root of 6 can be written in different ways.

Radical form: √6
Decimal form: 2.449
Exponent form: (6)^1/2

Is the Square Root of 6 Rational or Irrational?

The square root of 6 is an irrational number with non-terminating digits.
The square root of 6 cannot be written in the form of p/q. Hence, it is an irrational number.

How to find the Square Root of 6?

There are 2 main methods we use to find the square root of 6.

Prime Factorization
Long division

Prime Factorization

To find the square root of 6, we shall first express it in terms of its prime factors.
6 = 2 × 3
Now, let's find the square root.
√6 = √(2 × 3)
√6 = √2 × √3
= 1.414 × 1.732
= 2.449

Therefore, the square root of 6 is 2.449

Long Division

Step 1: Make a pair of digits (by placing a bar over them) from one's place as shown in the figure.
Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 6. We know that 2 × 2 = 4 which is less than 6. Place 2 in the quotient and divide 6 by 2 to get the remainder as 2.
Step 3: Place a decimal after the quotient as we are now dividing using the 0s from the decimal part of 6. Remember to drag down the pair of 0s, making the dividend 200. Also, adding 2 by itself gives us 4 which becomes the starting digit of our next divisor.
Step 4: Now we have 4X as our new divisor. We need to find the value of X such that 4X × X gives us a value less than 200. The number 4 fills the X position and therefore, the dividend is 44 and the quotient is now 2.4.
Step 5: The next divisor will be 44 + 4 and the dividend will be 2400. We will continue doing the same steps till we get the number of decimals we require.

So our long division now looks like this:

Square root of 6 using long division method

Therefore, the square root of 6 is 2.449

Explore square roots using illustrations and interactive examples

Important Notes

The square root of 6 = 2.449
√6 is irrational and is non-terminating.
The square root of 6 has 2 real roots, +2.449 and -2.449

Solved Examples

Example 1: Kate has a cube. The area of all 6 sides of the cube is 36 cm². Help her calculate the edge length of the cube.

Solution:

Total Surface Area is 36 cm²
Surface Area of each side = 36/6 = 6 cm²
Edge Length = Square root(6) = 2.45 cm
Therefore, the edge length of the cube is 2.45 cm.
Example 2: What will be the distance covered by a person running at 6√6 miles per hour in 1 hour?

Solution:

Distance covered = Speed × Time
Therefore, the person covers a total distance of 6√6 × 1 = 14.697 × 1 = 14.697 miles
Example: If the surface area of a sphere is 24π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 24π in²
⇒ r = ±√6 in
Since radius can't be negative,
⇒ r = √6
The square root of 6 is 2.449.
⇒ r = 2.449 in

go to slide go to slide go to slide

Have questions on basic mathematical concepts?

Become a problem-solving champ using logic, not rules. Learn the why behind math with our certified experts

Book a Free Trial Class

FAQs on the Square Root of 6

What is the Value of the Square Root of 6?

The square root of 6 is 2.44948.

Why is the Square Root of 6 an Irrational Number?

Upon prime factorizing 6 i.e. 2¹ × 3¹, 2 is in odd power. Therefore, the square root of 6 is irrational.

What is the Square Root of -6?

The square root of -6 is an imaginary number. It can be written as √-6 = √-1 × √6 = i √6 = 2.449i
where i = √-1 and it is called the imaginary unit.

Is the number 6 a Perfect Square?

The prime factorization of 6 = 2¹ × 3¹. Here, the prime factor 2 is not in the pair. Therefore, 6 is not a perfect square.

What is the Value of 1 square root 6?

The square root of 6 is 2.449. Therefore, 1 √6 = 1 × 2.449 = 2.449.

What is the Square of the Square Root of 6?

The square of the square root of 6 is the number 6 itself i.e. (√6)² = (6)^2/2 = 6.

Math worksheets and
visual curriculum