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Square Root of 269

The square root of 269 is expressed as √269 in the radical form and as (269)^½ or (269)^0.5 in the exponent form. The square root of 269 rounded up to 9 decimal places is 16.401219467. It is the positive solution of the equation x² = 269.

Square Root of 269: 16.401219466856727
Square Root of 269 in exponential form: (269)^½ or (269)^0.5
Square Root of 269 in radical form: √269

Square Root of 269

1.	What is the Square Root of 269?
2.	How to find the Square Root of 269?
3.	Is the Square Root of 269 Irrational?
4.	FAQs

What is the Square Root of 269?

The square root of 269, (or root 269), is the number which when multiplied by itself gives the product as 269. Therefore, the square root of 269 = √269 = 16.401219466856727.

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How to Find Square Root of 269?

Square Root of 269 by Long Division Method

Value of √269 by Long Division Method

Explanation:

Forming pairs: 02 and 69
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 69, to the right of the remainder 1. The new dividend is now 169.
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 <= 169. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 169.
Divide 169 by 26 with the quotient as 6, giving the remainder = 169 - 26 × 6 = 169 - 156 = 13.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 13. The new dividend is now 1300.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 4) such that 32Z × Z <= 1300. Together they form a new divisor (324) for the new dividend (1300).
Divide 1300 by 324 with the quotient as 4, giving the remainder = 1300 - 324 × 4 = 1300 - 1296 = 4.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 269.

Therefore, the square root of 269 by long division method is 16.4 approx.

Is Square Root of 269 Irrational?

The actual value of √269 is undetermined. The value of √269 up to 25 decimal places is 16.40121946685672516307471. Hence, the square root of 269 is an irrational number.

☛ Also Check:

Square Root of 113 - √113 = 10.63015
Square Root of 14 - √14 = 3.74166
Square Root of 140 - √140 = 11.83216
Square Root of 196 - √196 = 14
Square Root of 96 - √96 = 9.79796
Square Root of 60 - √60 = 7.74597
Square Root of 8 - √8 = 2.82843

Square Root of 269 Solved Examples

Example 1: Solve the equation x² − 269 = 0

Solution:

x² - 269 = 0 i.e. x² = 269
x = ±√269
Since the value of the square root of 269 is 16.401,
⇒ x = +√269 or -√269 = 16.401 or -16.401.
Example 2: If the area of a circle is 269π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 269π in²
⇒ r = ±√269 in
Since radius can't be negative,
⇒ r = √269
The square root of 269 is 16.401.
⇒ r = 16.401 in
Example 3: If the area of a square is 269 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 269 in²
⇒ a = ±√269 in
Since length can't be negative,
⇒ a = √269 = 16.401 in

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FAQs on the Square Root of 269

What is the Value of the Square Root of 269?

The square root of 269 is 16.40121.

Why is the Square Root of 269 an Irrational Number?

The number 269 is prime. This implies that the number 269 is pairless and is not in the power of 2. Therefore, the square root of 269 is irrational.

If the Square Root of 269 is 16.401. Find the Value of the Square Root of 2.69.

Let us represent √2.69 in p/q form i.e. √(269/100) = 2.69/10 = 1.640. Hence, the value of √2.69 = 1.640

What is the Square Root of 269 in Simplest Radical Form?

The number 269 is a prime number. This implies that the number 269 is pairless and is not in the power of 2. Therefore, the radical form of square root of 269 cannot be simplified further.

What is the Value of 19 square root 269?

The square root of 269 is 16.401. Therefore, 19 √269 = 19 × 16.401 = 311.623.

Evaluate 11 plus 15 square root 269

The given expression is 11 + 15 √269. We know that the square root of 269 is 16.401. Therefore, 11 + 15 √269 = 11 + 15 × 16.401 = 11 + 246.018 = 257.018

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