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Square Root of 241

The square root of 241 is expressed as √241 in the radical form and as (241)^½ or (241)^0.5 in the exponent form. The square root of 241 rounded up to 9 decimal places is 15.524174696. It is the positive solution of the equation x² = 241.

Square Root of 241: 15.524174696260024
Square Root of 241 in exponential form: (241)^½ or (241)^0.5
Square Root of 241 in radical form: √241

Square Root of 241

1.	What is the Square Root of 241?
2.	How to find the Square Root of 241?
3.	Is the Square Root of 241 Irrational?
4.	FAQs

What is the Square Root of 241?

The square root of 241, (or root 241), is the number which when multiplied by itself gives the product as 241. Therefore, the square root of 241 = √241 = 15.524174696260024.

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How to Find Square Root of 241?

Square Root of 241 by Long Division Method

Value of √241 by Long Division Method

Explanation:

Forming pairs: 02 and 41
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 41, to the right of the remainder 1. The new dividend is now 141.
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 5) such that 2Z × Z <= 141. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 141.
Divide 141 by 25 with the quotient as 5, giving the remainder = 141 - 25 × 5 = 141 - 125 = 16.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 16. The new dividend is now 1600.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 5) such that 30Z × Z <= 1600. Together they form a new divisor (305) for the new dividend (1600).
Divide 1600 by 305 with the quotient as 5, giving the remainder = 1600 - 305 × 5 = 1600 - 1525 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 241.

Therefore, the square root of 241 by long division method is 15.5 approx.

Is Square Root of 241 Irrational?

The actual value of √241 is undetermined. The value of √241 up to 25 decimal places is 15.52417469626002372886246. Hence, the square root of 241 is an irrational number.

☛ Also Check:

Square Root of 80 - √80 = 8.94427
Square Root of 625 - √625 = 25
Square Root of 225 - √225 = 15
Square Root of 73 - √73 = 8.54400
Square Root of 26 - √26 = 5.09902
Square Root of 76 - √76 = 8.71780
Square Root of 113 - √113 = 10.63015

Square Root of 241 Solved Examples

Example 1: Solve the equation x² − 241 = 0

Solution:

x² - 241 = 0 i.e. x² = 241
x = ±√241
Since the value of the square root of 241 is 15.524,
⇒ x = +√241 or -√241 = 15.524 or -15.524.
Example 2: If the surface area of a sphere is 964π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 964π in²
⇒ r = ±√241 in
Since radius can't be negative,
⇒ r = √241
The square root of 241 is 15.524.
⇒ r = 15.524 in
Example 3: If the area of a circle is 241π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 241π in²
⇒ r = ±√241 in
Since radius can't be negative,
⇒ r = √241
The square root of 241 is 15.524.
⇒ r = 15.524 in

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FAQs on the Square Root of 241

What is the Value of the Square Root of 241?

The square root of 241 is 15.52417.

Why is the Square Root of 241 an Irrational Number?

The number 241 is prime. This implies that the number 241 is pairless and is not in the power of 2. Therefore, the square root of 241 is irrational.

What is the Square Root of -241?

The square root of -241 is an imaginary number. It can be written as √-241 = √-1 × √241 = i √241 = 15.524i
where i = √-1 and it is called the imaginary unit.

Is the number 241 a Perfect Square?

The number 241 is prime. This implies that the square root of 241 cannot be expressed as a product of two equal integers. Therefore, the number 241 is not a perfect square.

Evaluate 10 plus 9 square root 241

The given expression is 10 + 9 √241. We know that the square root of 241 is 15.524. Therefore, 10 + 9 √241 = 10 + 9 × 15.524 = 10 + 139.718 = 149.718

If the Square Root of 241 is 15.524. Find the Value of the Square Root of 2.41.

Let us represent √2.41 in p/q form i.e. √(241/100) = 2.41/10 = 1.552. Hence, the value of √2.41 = 1.552

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