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Square root of 136

136 is the sum of the first 16 positive integers. 136 has 8 divisors and it is divisible by 8. Hence, it is a refactorable number. In this mini-lesson let us learn to calculate the square root of 136 and to express the square root of 136 in the simplest radical form.

  • Square Root of 136: √136 = 11.661
  • Square of 136: 1362 = 18,496
1. What Is the Square Root of 136?
2. Is Square Root of 136 Rational or Irrational?
3. How to Find the Square Root of 136?
4. Tips And Tricks
5. FAQs on Square Root of 136
6. Important Notes on Square Root of 136

What Is the Square Root of 136?

  • The square root of 136 is 136 raised to the power ½. 136½ = (number × number) ½ = √136
  • 11.661 × 11.661 = √136 and -11.661 × -11.661 = √136
  • √136 = ± 11.661

Is Square Root of 136 Rational or Irrational?

The square root of 136 is an irrational number where the numbers after the decimal point go up to infinity. √136 = 11.6619037897 which cannot be expressed as a rational number of the form p/q. Thus square root of 136 is an irrational number.

How to Find the Square Root of 136?

The square root of 136 or any number can be calculated in many ways. To mention a few: Prime factorization method, approximation method and the long division method.

Square Root of 136 in its simplest radical form

  • Prime factorization is expressing the number as a product of its prime factors. 136 = 2 × 2 × 2 × 17
  • √136 = √(2 × 2 × 2 × 17)
  • √136 = √(2 × 2 × 2 × 17) = 2 √34
  • Thus square root of 136 in its simplest radical form = 2 √34

Square Root of 136 by the Long Division Method

The long division method helps us to find the more accurate value of square root of any number.  Let's see how to find the square root of 136 by the long division method. Here are the desirable steps to be followed.

  • Write 136 as 1 36 00 00 00. Divide 1 by 1 and get the remaider as usual. Bring the pair of 36 down.
  • Multiply the quotient by 2 and have 2x as the new divisor. 
  • Find  a number in the place of x such that 2x × x gives 36 or less than that. We find 21 × 1 is 21. Subtract it from 36 and get the remainder as 15.
  • Multiply the quotient by 2 and have 22x as the new divisor.  Bring the pair of 00 down.
  • Find a number in the place of x such that 22x × x gives 15 00 or less than that. We find 226 × 6 is 1356. Subtract it from 1500 and get the remainder as 144.
  • Multiply the quotient by 2 and have 232x as the new divisor.  Bring the pair of 00 down.
  • Find a number in the place of x such that 232x × x gives 1 44 00 or less than that. We find 2326 × 6 is 13956. Subtract it from 1 44 00 and get the remainder as 4 44.
  • Repeat the process until we approximate to 3 decimal places.
  • Thus √136 = 11.661 to the nearest thousandths.

square root of 136 by division method

Explore Square roots using illustrations and interactive examples

Tips and Tricks

  • √136  lies between √121 and  √144. Clearly, √136 lies between 11 and 12. Divide √136 by 12 and get the quotient as 11.33. Find the average between 11.33 and 12 and obtain the value is 11.665 which is approximately equal to √136.

Important Notes

  • The square root of 136 is 11.661 approximated to 3 decimal places.
  • The simplified form of √136 in its radical form is 2√34.
  • √136 is an irrational number.
 

Square Root of 136 Solved Examples

 

  1. Example 1: Sia is creating a right triangle on her embroidery work. She makes the "L" shape with the thread running 10 inches down and 6 inches right. What will be the length of the third side to the nearest tenth?

    Solution: 

    The desired third side we are looking for is the hypotenuse. 
    102 + 62 = hypotenuse2
    hypotenuse2 = 100 + 36 = 136
    hypotenuse = √136 = 11.661
    Rounding it off to the nearest tenth, we get 11.6 inches.

  2.  

    Example 2: Stacey has a box that has the surface area of 1.36 square inches. What will be the area of the crepe paper she needs to buy to decor the top of the box?

    Solution: 

    Area = side × side 
    1.36 = side2
    side = √1. 36 = √136/√100 = √136/10 = 11.661/10 = 1.661 inches
    She needs to buy atleast a crepe that is 2 inches long.
    Therefore, the area of the crepe paper she needs to buy = side × side =  4 sq. inches

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FAQs On Square Root of 136

What is the square root of 136?

The square root of 136 is ±11.661.

How do you write square root of 136 in its simplified form?

2 √34 is the simplest form of 136.

136 is the square root of which number?

136 is the square root of 18,496.

Is square root of 136 a rational number?

square root of 136  is an irrational number, because the value of √136 is a non-teminating decimal. √136 = 11.6619037897

How to find the square root of √136?

The accurate value of √136 can be evaluated using the long division method.

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