A day full of math games & activities. Find one near you.

Square Root of 141

The square root of 141 is expressed as √141 in the radical form and as (141)^½ or (141)^0.5 in the exponent form. The square root of 141 rounded up to 6 decimal places is 11.874342. It is the positive solution of the equation x² = 141.

Square Root of 141: 11.874342087037917
Square Root of 141 in exponential form: (141)^½ or (141)^0.5
Square Root of 141 in radical form: √141

Square Root of 141

1.	What is the Square Root of 141?
2.	How to find the Square Root of 141?
3.	Is the Square Root of 141 Irrational?
4.	FAQs

What is the Square Root of 141?

The square root of 141, (or root 141), is the number which when multiplied by itself gives the product as 141. Therefore, the square root of 141 = √141 = 11.874342087037917.

☛ Check: Square Root Calculator

How to Find Square Root of 141?

Square Root of 141 by Long Division Method

Value of √141 by Long Division Method

Explanation:

Forming pairs: 01 and 41
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 41, to the right of the remainder 0. The new dividend is now 41.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 1) such that 2Z × Z <= 41. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 41.
Divide 41 by 21 with the quotient as 1, giving the remainder = 41 - 21 × 1 = 41 - 21 = 20.
Now, let's find the decimal places after the quotient 11.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 8) such that 22Z × Z <= 2000. Together they form a new divisor (228) for the new dividend (2000).
Divide 2000 by 228 with the quotient as 8, giving the remainder = 2000 - 228 × 8 = 2000 - 1824 = 176.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 141.

Therefore, the square root of 141 by long division method is 11.8 approx.

Is Square Root of 141 Irrational?

The actual value of √141 is undetermined. The value of √141 up to 25 decimal places is 11.87434208703791723467292. Hence, the square root of 141 is an irrational number.

☛ Also Check:

Square Root of 841 - √841 = 29
Square Root of 45 - √45 = 6.70820
Square Root of 2 - √2 = 1.41421
Square Root of 120 - √120 = 10.95445
Square Root of 361 - √361 = 19
Square Root of 1521 - √1521 = 39
Square Root of 35 - √35 = 5.91608

Square Root of 141 Solved Examples

Example 1: Solve the equation x² − 141 = 0

Solution:

x² - 141 = 0 i.e. x² = 141
x = ±√141
Since the value of the square root of 141 is 11.874,
⇒ x = +√141 or -√141 = 11.874 or -11.874.
Example 2: If the area of a circle is 141π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 141π in²
⇒ r = ±√141 in
Since radius can't be negative,
⇒ r = √141
The square root of 141 is 11.874.
⇒ r = 11.874 in
Example 3: If the area of an equilateral triangle is 141√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 141√3 in²
⇒ a = ±√564 in
Since length can't be negative,
⇒ a = √564 = 2 √141
We know that the square root of 141 is 11.874.
⇒ a = 23.749 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 141

What is the Value of the Square Root of 141?

The square root of 141 is 11.87434.

Why is the Square Root of 141 an Irrational Number?

Upon prime factorizing 141 i.e. 3¹ × 47¹, 3 is in odd power. Therefore, the square root of 141 is irrational.

Is the number 141 a Perfect Square?

The prime factorization of 141 = 3¹ × 47¹. Here, the prime factor 3 is not in the pair. Therefore, 141 is not a perfect square.

If the Square Root of 141 is 11.874. Find the Value of the Square Root of 1.41.

Let us represent √1.41 in p/q form i.e. √(141/100) = 1.41/10 = 1.187. Hence, the value of √1.41 = 1.187

What is the Square of the Square Root of 141?

The square of the square root of 141 is the number 141 itself i.e. (√141)² = (141)^2/2 = 141.

Evaluate 20 plus 11 square root 141

The given expression is 20 + 11 √141. We know that the square root of 141 is 11.874. Therefore, 20 + 11 √141 = 20 + 11 × 11.874 = 20 + 130.618 = 150.618

Math worksheets and
visual curriculum