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Square Root of 140

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.

Square Root of 140: 11.832159566199232
Square Root of 140 in exponential form: (140)^½ or (140)^0.5
Square 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) = 2√35

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 2√35.

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.

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?

Example 1: What are the two consecutive numbers between which the value of square root of 140 lies?

Solution

The perfect squares closer to 140 are 121 and 144. The square root of 121 is 11 and the square root of 144 is 12. Hence, the two numbers between which the square root of 140 lies are 11 and 12.
Example 2: What is the circumference of a circle if the area of the circle is 140π square inches?

Solution

The area of circle is given as πr².
Hence, area = πr² = 140π ⇒ r² = 140 ⇒ r = √140 = 11.83 ≈ 11.8 inches.
Circumference of circle = 2πr = 2 × π × 11.8 = 74.14 inches. Hence, the circumference of circle if the area of circle is 140π square inches is 74.14 inches.
Example: If the area of a circle is 140π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 140π in²
⇒ r = ±√140 in
Since radius can't be negative,
⇒ r = √140
The square root of 140 is 11.832.
⇒ r = 11.832 in

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FAQs on the Square Root of 140

What is the Value of the Square Root of 140?

The square root of 140 is 11.83215.

Why is the Square Root of 140 an Irrational Number?

Upon prime factorizing 140 i.e. 2² × 5¹ × 7¹, 5 is in odd power. Therefore, the square root of 140 is irrational.

If the Square Root of 140 is 11.832. Find the Value of the Square Root of 1.4.

Let us represent √1.4 in p/q form i.e. √(140/100) = 1.4/10 = 1.183. Hence, the value of √1.4 = 1.183

What is the Value of 10 square root 140?

The square root of 140 is 11.832. Therefore, 10 √140 = 10 × 11.832 = 118.322.

What is the Square Root of 140 in Simplest Radical Form?

We need to express 140 as the product of its prime factors i.e. 140 = 2 × 2 × 5 × 7. Therefore, √140 = √2 × 2 × 5 × 7 = 2 √35. Thus, the square root of 140 in the lowest radical form is 2 √35.

Evaluate 5 plus 7 square root 140

The given expression is 5 + 7 √140. We know that the square root of 140 is 11.832. Therefore, 5 + 7 √140 = 5 + 7 × 11.832 = 5 + 82.825 = 87.825

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