The square root of 140 is expressed as √140 in the radical form and as (140)½ or (140)0.5 in the exponent form. The square root of 140 rounded up to 7 decimal places is 11.8321596. It is the positive solution of the equation x2 = 140. We can express the square root of 140 in its lowest radical form as 2 √35.

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Square Root of 140: 11.832159566199232Square Root of 140 in exponential form: (140)½ or (140)0.5Square Root of 140 in radical form: √140 or 2 √35
1.What Is the Square Root of 140?
2.Is Square Root of 140 Rational or Irrational?
3.Tips and Tricks
4.How to Find the Square Root of 140?
5.FAQs on Square Root of 140

What Is the Square Root of 140?


The square root of 140 is the number which, when multiplied to itself, gives the product as 140. Since there is no such integer which on product with itself gives 140 exactly, the square root of 140 is not a whole number. 


Is the Square Root of 140 Rational or Irrational?


The square root of 140 is 11.8321595 (approximately). It is a non-recurring and non-terminating decimal number. This shows that 140 is not a perfect square, which also proves that the square root of 140 is an irrational number.

Tips and Tricks:

The square root of any number n, which is not a perfect square, is always an irrational number. As 140 is not a perfect square, the square root of 140 is an irrational number.

How to Find the Square Root of 140?

To find the square root of 140, we use the following steps:

Step 1: First we check whether the number is a perfect square or not. 140 is not a perfect square as it cannot be expressed as a product of two same numbers.Step 2: Once the number is checked, we can follow the steps as per the conditions written below:A perfect square number can be written as x2 = x.For a non-perfect square number, the square root can be found using the long division method. This number can be written in its simplified radical form of the square root.

As 140 is not a perfect square, the square root of 140 is found using the long division method. The simplified radical form of the square root of 140 is given below.

Simplified Radical Form of Square Root of 140

140 is expressed as the product of 20 and 7. It is given as:

140 = (20 × 7) = (4 × 5 × 7) = 235

As 7 is not a perfect square, it stays within the root sign. 20 can be written as 4 × 5. Thus, the simplified radical form of the square root of 140 is 235.

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Square Root of 140 by Long Division Method

The square root of 140 is found using the long division method. The steps to be followed are: 

Step 1: We start pairing from the right and pair up the digits by putting a bar above them.Step 2: We find a number which on multiplication with itself, gives a product less than or equal to 1. Keeping the divisor as 1, we get the quotient as 1 and the remainder as 1-1 = 0. Step 3: Double the divisor and enter it with a blank on its right. Then assume the largest digit to replace the blank. This will become the new digit in the quotient. Now, when the new divisor will be multiplied to the new quotient, the final product will be lesser than or equal to our dividend. Finally, divide and write the remainder. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want. 

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Hence, √140 = 11.832

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Challenging Questions:

How will Christie find the square root of 140 using the long division method up to 8 decimal places?How will Mandy express the square root of 280 in terms of square root of 140?