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Square Root of 259

The square root of 259 is expressed as √259 in the radical form and as (259)^½ or (259)^0.5 in the exponent form. The square root of 259 rounded up to 10 decimal places is 16.0934769394. It is the positive solution of the equation x² = 259.

Square Root of 259: 16.09347693943108
Square Root of 259 in exponential form: (259)^½ or (259)^0.5
Square Root of 259 in radical form: √259

Square Root of 259

1.	What is the Square Root of 259?
2.	How to find the Square Root of 259?
3.	Is the Square Root of 259 Irrational?
4.	FAQs

What is the Square Root of 259?

The square root of 259, (or root 259), is the number which when multiplied by itself gives the product as 259. Therefore, the square root of 259 = √259 = 16.09347693943108.

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How to Find Square Root of 259?

Square Root of 259 by Long Division Method

Value of √259 by Long Division Method

Explanation:

Forming pairs: 02 and 59
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 59, to the right of the remainder 1. The new dividend is now 159.
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 <= 159. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 159.
Divide 159 by 26 with the quotient as 6, giving the remainder = 159 - 26 × 6 = 159 - 156 = 3.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 3. The new dividend is now 300.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 0) such that 32Z × Z <= 300. Together they form a new divisor (320) for the new dividend (300).
Divide 300 by 320 with the quotient as 0, giving the remainder = 300 - 320 × 0 = 300 - 0 = 300.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 259.

Therefore, the square root of 259 by long division method is 16.0 approx.

Is Square Root of 259 Irrational?

The actual value of √259 is undetermined. The value of √259 up to 25 decimal places is 16.09347693943108118684999. Hence, the square root of 259 is an irrational number.

☛ Also Check:

Square Root of 98 - √98 = 9.89949
Square Root of 92 - √92 = 9.59166
Square Root of 2 - √2 = 1.41421
Square Root of 61 - √61 = 7.81025
Square Root of 99 - √99 = 9.94987
Square Root of 10 - √10 = 3.16228
Square Root of 106 - √106 = 10.29563

Square Root of 259 Solved Examples

Example 1: Solve the equation x² − 259 = 0

Solution:

x² - 259 = 0 i.e. x² = 259
x = ±√259
Since the value of the square root of 259 is 16.093,
⇒ x = +√259 or -√259 = 16.093 or -16.093.
Example 2: If the surface area of a sphere is 1036π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1036π in²
⇒ r = ±√259 in
Since radius can't be negative,
⇒ r = √259
The square root of 259 is 16.093.
⇒ r = 16.093 in
Example 3: If the area of a circle is 259π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 259π in²
⇒ r = ±√259 in
Since radius can't be negative,
⇒ r = √259
The square root of 259 is 16.093.
⇒ r = 16.093 in

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FAQs on the Square Root of 259

What is the Value of the Square Root of 259?

The square root of 259 is 16.09347.

Why is the Square Root of 259 an Irrational Number?

Upon prime factorizing 259 i.e. 7¹ × 37¹, 7 is in odd power. Therefore, the square root of 259 is irrational.

What is the Square Root of 259 in Simplest Radical Form?

We need to express 259 as the product of its prime factors i.e. 259 = 7 × 37. Therefore, as visible, the radical form of the square root of 259 cannot be simplified further. Therefore, the simplest radical form of the square root of 259 can be written as √259

If the Square Root of 259 is 16.093. Find the Value of the Square Root of 2.59.

Let us represent √2.59 in p/q form i.e. √(259/100) = 2.59/10 = 1.609. Hence, the value of √2.59 = 1.609

Evaluate 20 plus 14 square root 259

The given expression is 20 + 14 √259. We know that the square root of 259 is 16.093. Therefore, 20 + 14 √259 = 20 + 14 × 16.093 = 20 + 225.309 = 245.309

What is the Value of 7 square root 259?

The square root of 259 is 16.093. Therefore, 7 √259 = 7 × 16.093 = 112.654.

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