Square root of 116

  ±10.77 is the square root of 116. To find the square root, we should use the inverse process of squaring a number. So, when 10.77 is squared, we get 116. The radical form of 116 is expressed as √116, where ‘√’ is the radical symbol. The square root of 116 is expressed in its exponential form as (116)^½.

The square root of 116 can be calculated with the help of different methods such as:

• Prime Factorization Method

• Long Division Method

• Approximation or Estimation Method
   

The prime factorization of 116 is done by breaking 116 into its prime factors until the quotient can’t be divided anymore. 

The prime factors of 116 are 2 and 29, expressed as 2×2×29  → 2² × 29

If a number exists that cannot be paired, then that number is written using the radical sign along with paired numbers. Hence, 2√29 is the simplest form of √116.

The long division method is used to find the square root of non-perfect squares. This method involves dividing the dividend with divisors, which results in not just a quotient but also a remainder.

To calculate √116:

Step 1: Draw a horizontal above 116

Step 2: Now find the closest perfect square that lies near to 116. The perfect square closest to 116 is 100  → 10²

Step 3: Divide 116 by 10. The quotient will remain 10 and the remainder will be 16 (116-100)

Step 4: Bring down the remainder 16 and add two zeros. Add a decimal point to the quotient, it turns to 10.0.

Step 5: Double the quotient and use it as the new divisor. Now pick a number that will complete the divisor so that when it is multiplied by, the product is less than or equal to 1600. 

Step 6: Continue to the division to find the √116

The approximation method estimates the square root by considering the closest perfect square.

Step 1: Nearest perfect square to 116 is √100=10 and √121=11

Step 2: 116 falls between 100 and 121 therefore the square root falls between 10 and 11

Step 3:  We find that  √116 = 10.77.
 

• Prime number: Numbers having two factors.

• Perfect square: Numbers whose square root include only whole numbers

• Prime Factorization:  Process of expressing the product of prime numbers in exponential form.

• Non-perfect square: Numbers whose square root contains decimals.