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

Square Root of 118

The square root of 118 is expressed as √118 in the radical form and as (118)^½ or (118)^0.5 in the exponent form. The square root of 118 rounded up to 6 decimal places is 10.862780. It is the positive solution of the equation x² = 118.

Square Root of 118: 10.862780491200215
Square Root of 118 in exponential form: (118)^½ or (118)^0.5
Square Root of 118 in radical form: √118

Square Root of 118

1.	What is the Square Root of 118?
2.	How to find the Square Root of 118?
3.	Is the Square Root of 118 Irrational?
4.	FAQs

What is the Square Root of 118?

The square root of 118, (or root 118), is the number which when multiplied by itself gives the product as 118. Therefore, the square root of 118 = √118 = 10.862780491200215.

☛ Check: Square Root Calculator

How to Find Square Root of 118?

Square Root of 118 by Long Division Method

Value of √118 by Long Division Method

Explanation:

Forming pairs: 01 and 18
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 18, to the right of the remainder 0. The new dividend is now 18.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 0) such that 2Z × Z <= 18. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 18.
Divide 18 by 20 with the quotient as 0, giving the remainder = 18 - 20 × 0 = 18 - 0 = 18.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 18. The new dividend is now 1800.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 8) such that 20Z × Z <= 1800. Together they form a new divisor (208) for the new dividend (1800).
Divide 1800 by 208 with the quotient as 8, giving the remainder = 1800 - 208 × 8 = 1800 - 1664 = 136.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 118.

Therefore, the square root of 118 by long division method is 10.8 approximately.

Is Square Root of 118 Irrational?

The actual value of √118 is undetermined. The value of √118 up to 25 decimal places is 10.86278049120021572389149. Hence, the square root of 118 is an irrational number.

☛ Also Check:

Square Root of 512 - √512 = 22.62742
Square Root of 325 - √325 = 18.02776
Square Root of 29 - √29 = 5.38516
Square Root of 1681 - √1681 = 41
Square Root of 25 - √25 = 5
Square Root of 35 - √35 = 5.91608
Square Root of 324 - √324 = 18

Square Root of 118 Solved Examples

Example 1: Solve the equation x² − 118 = 0

Solution:

x² - 118 = 0 i.e. x² = 118
x = ±√118
Since the value of the square root of 118 is 10.863,
⇒ x = +√118 or -√118 = 10.863 or -10.863.
Example 2: If the area of a circle is 118π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 118π in²
⇒ r = ±√118 in
Since radius can't be negative,
⇒ r = √118
The square root of 118 is 10.863.
⇒ r = 10.863 in
Example 3: If the surface area of a sphere is 472π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 472π in²
⇒ r = ±√118 in
Since radius can't be negative,
⇒ r = √118
The square root of 118 is 10.863.
⇒ r = 10.863 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 118

What is the Value of the Square Root of 118?

The square root of 118 is 10.86278.

Why is the Square Root of 118 an Irrational Number?

Upon prime factorizing 118 i.e. 2¹ × 59¹, 2 is in odd power. Therefore, the square root of 118 is irrational.

Is the number 118 a Perfect Square?

The prime factorization of 118 = 2¹ × 59¹. Here, the prime factor 2 is not in the pair. Therefore, 118 is not a perfect square.

If the Square Root of 118 is 10.863. Find the Value of the Square Root of 1.18.

Let us represent √1.18 in p/q form i.e. √(118/100) = 1.18/10 = 1.086. Hence, the value of √1.18 = 1.086

What is the Square of the Square Root of 118?

The square of the square root of 118 is the number 118 itself i.e. (√118)² = (118)^2/2 = 118.

Evaluate 12 plus 5 square root 118

The given expression is 12 + 5 √118. We know that the square root of 118 is 10.863. Therefore, 12 + 5 √118 = 12 + 5 × 10.863 = 12 + 54.314 = 66.314

Math worksheets and
visual curriculum