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Square Root of 261

The square root of 261 is expressed as √261 in the radical form and as (261)^½ or (261)^0.5 in the exponent form. The square root of 261 rounded up to 9 decimal places is 16.155494421. It is the positive solution of the equation x² = 261. We can express the square root of 261 in its lowest radical form as 3 √29.

Square Root of 261: 16.15549442140351
Square Root of 261 in exponential form: (261)^½ or (261)^0.5
Square Root of 261 in radical form: √261 or 3 √29

Square Root of 261

1.	What is the Square Root of 261?
2.	How to find the Square Root of 261?
3.	Is the Square Root of 261 Irrational?
4.	FAQs

What is the Square Root of 261?

The square root of 261, (or root 261), is the number which when multiplied by itself gives the product as 261. Therefore, the square root of 261 = √261 = 3 √29 = 16.15549442140351.

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How to Find Square Root of 261?

Square Root of 261 by Long Division Method

Value of √261 by Long Division Method

Explanation:

Forming pairs: 02 and 61
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 61, to the right of the remainder 1. The new dividend is now 161.
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 6) such that 2Z × Z <= 161. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 161.
Divide 161 by 26 with the quotient as 6, giving the remainder = 161 - 26 × 6 = 161 - 156 = 5.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 5. The new dividend is now 500.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 1) such that 32Z × Z <= 500. Together they form a new divisor (321) for the new dividend (500).
Divide 500 by 321 with the quotient as 1, giving the remainder = 500 - 321 × 1 = 500 - 321 = 179.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 261.

Therefore, the square root of 261 by long division method is 16.1 approximately.

Is Square Root of 261 Irrational?

The actual value of √261 is undetermined. The value of √261 up to 25 decimal places is 16.15549442140351209375213. Hence, the square root of 261 is an irrational number.

☛ Also Check:

Square Root of 33 - √33 = 5.74456
Square Root of 90 - √90 = 9.48683
Square Root of 44 - √44 = 6.63325
Square Root of 48 - √48 = 6.92820
Square Root of 73 - √73 = 8.54400
Square Root of 75 - √75 = 8.66025
Square Root of 13 - √13 = 3.60555

Square Root of 261 Solved Examples

Example 1: Solve the equation x² − 261 = 0

Solution:

x² - 261 = 0 i.e. x² = 261
x = ±√261
Since the value of the square root of 261 is 16.155,
⇒ x = +√261 or -√261 = 16.155 or -16.155.
Example 2: If the surface area of a sphere is 1044π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1044π in²
⇒ r = ±√261 in
Since radius can't be negative,
⇒ r = √261
The square root of 261 is 16.155.
⇒ r = 16.155 in
Example 3: If the surface area of a cube is 1566 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1566 in²
⇒ a = ±√261 in
Since length can't be negative,
⇒ a = √261
We know that the square root of 261 is 16.155.
⇒ a = 16.155 in

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FAQs on the Square Root of 261

What is the Value of the Square Root of 261?

The square root of 261 is 16.15549.

Why is the Square Root of 261 an Irrational Number?

Upon prime factorizing 261 i.e. 3² × 29¹, 29 is in odd power. Therefore, the square root of 261 is irrational.

What is the Square Root of 261 in Simplest Radical Form?

We need to express 261 as the product of its prime factors i.e. 261 = 3 × 3 × 29. Therefore, √261 = √3 × 3 × 29 = 3 √29. Thus, the square root of 261 in the lowest radical form is 3 √29.

If the Square Root of 261 is 16.155. Find the Value of the Square Root of 2.61.

Let us represent √2.61 in p/q form i.e. √(261/100) = 2.61/10 = 1.616. Hence, the value of √2.61 = 1.616

Is the number 261 a Perfect Square?

The prime factorization of 261 = 3² × 29¹. Here, the prime factor 29 is not in the pair. Therefore, 261 is not a perfect square.

What is the Square of the Square Root of 261?

The square of the square root of 261 is the number 261 itself i.e. (√261)² = (261)^2/2 = 261.

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