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

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

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.

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.

Explore Square roots using illustrations and interactive examples

• Square root of 36
• Square root of 54
• Square root of 16
• Square root of 26
• Square root of 60

• √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.

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.