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

Square Root of 110

The square root of 110 is expressed as √110 in the radical form and as (110)^½ or (110)^0.5 in the exponent form. The square root of 110 rounded up to 8 decimal places is 10.48808848. It is the positive solution of the equation x² = 110.

Square Root of 110: 10.488088481701515
Square Root of 110 in exponential form: (110)^½ or (110)^0.5
Square Root of 110 in radical form: √110

1.	What Is the Square Root of 110?
2.	Is Square Root of 110 Rational or Irrational?
3.	How to Find the Square Root of 110?
4.	FAQs on Square Root of 110

What Is the Square Root of 110?

The square root of a number is the number that gets multiplied to itself to give the product. Hence, the square root of 110 is the value obtained after performing the operation of square root on 110.

Is the Square Root of 110 Rational or Irrational?

A number that can be written as the ratio of two integers, that is, p/q, such that q is not equal to 0 is called a rational number. 110 cannot be broken into two same factors which on squaring give the product as 110. It can be approximately written as a square of 10.488, which is a non-recurring and non-terminating decimal number.Hence, 110 is not a perfect square which also proves that it is an irrational number.

Tips and Tricks:

110 is a non-perfect square number. Thus square root of 110 would be an irrational number. We can conclude that the square root of any number "n," which is not a perfect square, will always be an irrational number.

How to Find the Square Root of 110?

There are different ways to calculate the square root of 110. Let us see how to represent square root of 110 in its simplified radical form.

Simplified Radical Form of Square Root of 110

The simplified radical form of square root of 110 is given as √110. 110 is expressed as 110 = 2 × 5 × 11. On taking square root of 110 we get, √110 = √( 2 × 5 × 11). We can see that there is no number which repeats within the square root. Hence, the simplified radical form of square root of 110 is √110. Let us now try finding the square root of 110 by the long division method.

Square Root of 110 by Long Division Method

Let us understand the process of finding square root of 110 by long division.

Step 1: First we pair the digits of 110 starting with a digit at one's place and put a horizontal bar to indicate pairing.
Step 2: Now we find a number which on multiplication with itself gives a product of less than or equal to 1. As we know 1 × 1 = 1 = 1.
Step 3: Now, we have to bring down 1 and multiply the quotient by 2. This give us 2. Hence, 2 is the starting digit of the new divisor.
Step 4: 0 is placed at one's place of new divisor because when 20 is multiplied by 0 we get 0. The obtained answer now is 1 and we bring down 00.
Step 5: The quotient now becomes 10 and it is multiplied by 2. This gives 20, which then would become the starting digit of the new divisor.
Step 6: 4 is placed at one's place of new divisor because on multiplying 204 by 4 we get 816. The answer now obtained is 184 and we bring 00 down.
Step 7: Now the quotient is 104 when multiplied by 2 gives 208, which will be the starting digit of the new divisor.
Step 8: 8 is placed at one's place of the divisor because on multiplying 2088 by 8 we will get 16704. The answer obtained is 1696 and we bring 00 down.
Step 9: Now the quotient is 1048 when multiplied by 2 gives 2096, which will be the starting digit of the new divisor.
Step 10: 8 is placed at one's place of the divisor because on multiplying 20968 by 8, we will get 167744. The answer obtained is 1856.

Square Root of 110 by Long Division

On repeating the steps we can estimate the value of square root of 110 to as many places as required.

Explore square roots using illustrations and interactive examples

Important Notes:

The square root is the inverse operation of squaring.
The square root of 110 can be expressed as √110 or (110)^1/2.
To find the square root of 110 or any other number, we can use the radical form and the long division method.

Example 1: Evaluate whether 110 = √100 + √10 or not.

Solution

On simplifying LHS we get, √110 = 10.488.
Similarly on simplifying RHS we get, √100 + √10 = 10 + 3.162 = 13.162.
Hence, √110 ≠ √100 + √10.
Example 2: What is the circumference of circle if the area of circle is 110π square inches?

Solution

The area of circle is given as πr².
Hence, area = πr² = 110π ⇒ r² = 110 ⇒ r = √110 = 10.48 ≈ 10.5 inches. Circumference of circle = 2πr = 2 × π × 10.5 = 65.94 inches.
Hence, the circumference of circle if the area of circle is 110π square inches is 65.94 inches.
Example 3: If the surface area of a sphere is 440π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 440π in²
⇒ r = ±√110 in
Since radius can't be negative,
⇒ r = √110
The square root of 110 is 10.488.
⇒ r = 10.488 in

go to slide go to slide go to slide

Breakdown tough concepts through simple visuals.

Math will no longer be a tough subject, especially when you understand the concepts through visualizations.

Book a Free Trial Class

FAQs on the Square Root of 110

What is the Value of the Square Root of 110?

The square root of 110 is 10.48808.

Why is the Square Root of 110 an Irrational Number?

Upon prime factorizing 110 i.e. 2¹ × 5¹ × 11¹, 2 is in odd power. Therefore, the square root of 110 is irrational.

Evaluate 6 plus 17 square root 110

The given expression is 6 + 17 √110. We know that the square root of 110 is 10.488. Therefore, 6 + 17 √110 = 6 + 17 × 10.488 = 6 + 178.298 = 184.298

What is the Square of the Square Root of 110?

The square of the square root of 110 is the number 110 itself i.e. (√110)² = (110)^2/2 = 110.

What is the Value of 13 square root 110?

The square root of 110 is 10.488. Therefore, 13 √110 = 13 × 10.488 = 136.345.

If the Square Root of 110 is 10.488. Find the Value of the Square Root of 1.1.

Let us represent √1.1 in p/q form i.e. √(110/100) = 1.1/10 = 1.049. Hence, the value of √1.1 = 1.049

Math worksheets and
visual curriculum