Square Root of 115
115 is an odd composite number and a semiprime number. Finding the squares and the square roots are the two inverse processes to each other. The square root of 115 can be written as 115 raised to the power half. In this mini lesson, let us learn about the square root of 115 and learn to find the square root of 115 by long division method.
 Square Root of 115: √115 = 10.723
 Square of 115: 115^{2} = 13,225
1.  What Is the Square Root of 115? 
2.  Is Square Root of 115 Rational or Irrational? 
3.  How to Find the Square Root of 115? 
4.  FAQs on Square Root of 115 
What Is the Square Root of 115?
 The square root of 115 can be written as √115 in its simplest radical form and (115)^{½ }in the exponential form.
 It means that there is a number a such that: a × a = 115. Now it can also be written as: a^{2} = 115 ⇒ a = √115.
 a is the 2nd root of 115 and a = ± 10.723.
Is Square Root of 115 Rational or Irrational?
The square root of 115 is an irrational number where the numbers after the decimal point go up to infinity. √115 = 10.72380529476361. √115 cannot be written in the form of p/q, hence it is an irrational number.
How to Find the Square Root of 115?
The square root of 115 or any number can be calculated in many ways. Two of them are the average method and the long division method.
Square Root of 115 by Average Method
 Take two perfect square numbers, one of which is just smaller than 115 and the other just greater than 115. It is written as:
√100 < √115 < √121 ⇒ 10 < √ 115 < 11  Divide 115 by 11
 Let us divide by 8 ⇒ 115 ÷ 11 = 10.45
 Find the average of 10.45 and 11
 (10.45 + 11)/2 = 21.45 ÷ 2 = 10.725
 Hence, √115 ≈ 10.725
Square Root of 115 by the Long Division Method
The long division method helps us find the more accurate value of square root of any number. Let's see how to find the square root of 115 by the long division method.
 Step 1: Express 115 as 115.000000. We take the number in pairs from the right. Take 1 as the dividend.
 Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 1 and as we know 1 × 1 = 1.
 Step 3: Now double the quotient obtained in step 2. Here is 1 × 2 = 2. 20 becomes the new divisor.
 Step 4: Bring down 15. We have 1500 as the dividend now. Find a (number + 20) × number ≤ 15. We cannot find any. Hence bring down the next pair of zeros.
 Step 5: We need to choose a number that while adding to 140 and multiplying the sum with the same number we get a number less than 600. 20+ 4 =144 and 164× 4 = 576. Subtract 576 from 600. We get 24.
 Step 6: Bring down the next pair of zeros. 2400 is the new dividend. Double the quotient. Here it is 148. Have it as 1480. Now find a number at the unit's place of 1480 multiplied by itself gives 2400 or less. We find that 1481 × 1 = 1481. Find the remainder.
 Step 6: Repeat the process until we get the remainder equal to zero. The square root of 115 up to two places is obtained by the long division method. Thus, √115 = 7.416.
Explore square roots using illustrations and interactive examples.
 Square root of 116
 Square root of 113
 Square root of 112
 Square root of 110
 Square root of 117
 Square root of 1156
Challenging Questions
 Find 1.15^{2} × √1.15
 Evaluate the square root of 115 up to 7 decimal places.
Important Notes
 The square root of 115 is √115 in the radical form, 115^{½} in the exponential form, and 10.723 in the decimal form.
 √115 is an irrational number.
Square Root of 115 Solved Examples

Example 1: Evaluate: √115 + √345
Solution:
√115 = √(5 × 23) and √345 = √(15 × 23) = √(5 × 3 × 23)
⇒ √115 + √343 = √(5 × 23) + √(5 × 3 × 23) = (√(5 × 23))(√3 + 1) = √115(√3 + 1)
Hence, √115 + √345 = √115(√3 + 1). 
Example 2: If the length of the carpet is twice its width and its area is 230 sq yards, how long is the carpet? Approximate to the nearest hundredth.
Solution:
Area of the carpet = length × width sq yards
Given length = 2 × width yards
Thus Area = (2 × width) × width
Area = 2 width^{2}
230 = 2 width^{2}
width^{2 }= 230 ÷ 2 = 115
width = √115 yards
width = √115 = 10.725 yards
⇒ length = 2 × 10.725 yards = 21.45 yards.Hence, the length of the carpet is 21.45 yards when approximated to nearest hundredth.
FAQs on Square Root of 115
What is the square root of 115?
The square root of 115 is approximately equal to 10.723.
How do you write square root of 115 in its simplified form?
The square root of 115 in its simplified form is written as √115.
Is the square root of 115 real?
Yes, the square root of 115 is real.
Is √115 a rational number?
No, √115 is an irrational number, because the value of √115 is a nonteminating decimal on evalulation.
How to find the square root of 115?
There are different methods to obtain the value of square root of 115. The most accurate value of √115 can be evaluated using the long division method.
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