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Square Root of 281

The square root of 281 is expressed as √281 in the radical form and as (281)^½ or (281)^0.5 in the exponent form. The square root of 281 rounded up to 8 decimal places is 16.76305461. It is the positive solution of the equation x² = 281.

Square Root of 281: 16.76305461424021
Square Root of 281 in exponential form: (281)^½ or (281)^0.5
Square Root of 281 in radical form: √281

Square Root of 281

1.	What is the Square Root of 281?
2.	How to find the Square Root of 281?
3.	Is the Square Root of 281 Irrational?
4.	FAQs

What is the Square Root of 281?

The square root of 281, (or root 281), is the number which when multiplied by itself gives the product as 281. Therefore, the square root of 281 = √281 = 16.76305461424021.

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How to Find Square Root of 281?

Square Root of 281 by Long Division Method

Value of √281 by Long Division Method

Explanation:

Forming pairs: 02 and 81
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 81, to the right of the remainder 1. The new dividend is now 181.
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 <= 181. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 181.
Divide 181 by 26 with the quotient as 6, giving the remainder = 181 - 26 × 6 = 181 - 156 = 25.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 7) such that 32Z × Z <= 2500. Together they form a new divisor (327) for the new dividend (2500).
Divide 2500 by 327 with the quotient as 7, giving the remainder = 2500 - 327 × 7 = 2500 - 2289 = 211.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 281.

Therefore, the square root of 281 by long division method is 16.7 approx.

Is Square Root of 281 Irrational?

The actual value of √281 is undetermined. The value of √281 up to 25 decimal places is 16.76305461424021012844570. Hence, the square root of 281 is an irrational number.

☛ Also Check:

Square Root of 784 - √784 = 28
Square Root of 35 - √35 = 5.91608
Square Root of 361 - √361 = 19
Square Root of 27 - √27 = 5.19615
Square Root of 288 - √288 = 16.97056
Square Root of 45 - √45 = 6.70820
Square Root of 2 - √2 = 1.41421

Square Root of 281 Solved Examples

Example 1: Solve the equation x² − 281 = 0

Solution:

x² - 281 = 0 i.e. x² = 281
x = ±√281
Since the value of the square root of 281 is 16.763,
⇒ x = +√281 or -√281 = 16.763 or -16.763.
Example 2: If the area of a circle is 281π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 281π in²
⇒ r = ±√281 in
Since radius can't be negative,
⇒ r = √281
The square root of 281 is 16.763.
⇒ r = 16.763 in
Example 3: If the area of an equilateral triangle is 281√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 = 281√3 in²
⇒ a = ±√1124 in
Since length can't be negative,
⇒ a = √1124 = 2 √281
We know that the square root of 281 is 16.763.
⇒ a = 33.526 in

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FAQs on the Square Root of 281

What is the Value of the Square Root of 281?

The square root of 281 is 16.76305.

Why is the Square Root of 281 an Irrational Number?

The number 281 is prime. This implies that the number 281 is pairless and is not in the power of 2. Therefore, the square root of 281 is irrational.

Evaluate 18 plus 15 square root 281

The given expression is 18 + 15 √281. We know that the square root of 281 is 16.763. Therefore, 18 + 15 √281 = 18 + 15 × 16.763 = 18 + 251.446 = 269.446

What is the Square Root of -281?

The square root of -281 is an imaginary number. It can be written as √-281 = √-1 × √281 = i √281 = 16.763i
where i = √-1 and it is called the imaginary unit.

Is the number 281 a Perfect Square?

The number 281 is prime. This implies that the square root of 281 cannot be expressed as a product of two equal integers. Therefore, the number 281 is not a perfect square.

What is the Value of 7 square root 281?

The square root of 281 is 16.763. Therefore, 7 √281 = 7 × 16.763 = 117.341.

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