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Square Root of 273

The square root of 273 is expressed as √273 in the radical form and as (273)^½ or (273)^0.5 in the exponent form. The square root of 273 rounded up to 6 decimal places is 16.522712. It is the positive solution of the equation x² = 273.

Square Root of 273: 16.522711641858304
Square Root of 273 in exponential form: (273)^½ or (273)^0.5
Square Root of 273 in radical form: √273

Square Root of 273

1.	What is the Square Root of 273?
2.	How to find the Square Root of 273?
3.	Is the Square Root of 273 Irrational?
4.	FAQs

What is the Square Root of 273?

The square root of 273, (or root 273), is the number which when multiplied by itself gives the product as 273. Therefore, the square root of 273 = √273 = 16.522711641858304.

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How to Find Square Root of 273?

Square Root of 273 by Long Division Method

Value of √273 by Long Division Method

Explanation:

Forming pairs: 02 and 73
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 73, to the right of the remainder 1. The new dividend is now 173.
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 <= 173. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 173.
Divide 173 by 26 with the quotient as 6, giving the remainder = 173 - 26 × 6 = 173 - 156 = 17.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 17. The new dividend is now 1700.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 5) such that 32Z × Z <= 1700. Together they form a new divisor (325) for the new dividend (1700).
Divide 1700 by 325 with the quotient as 5, giving the remainder = 1700 - 325 × 5 = 1700 - 1625 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 273.

Therefore, the square root of 273 by long division method is 16.5 approximately.

Is Square Root of 273 Irrational?

The actual value of √273 is undetermined. The value of √273 up to 25 decimal places is 16.52271164185830606181743. Hence, the square root of 273 is an irrational number.

☛ Also Check:

Square Root of 225 - √225 = 15
Square Root of 14 - √14 = 3.74166
Square Root of 36 - √36 = 6
Square Root of 900 - √900 = 30
Square Root of 16 - √16 = 4
Square Root of 77 - √77 = 8.77496
Square Root of 10 - √10 = 3.16228

Square Root of 273 Solved Examples

Example 1: Solve the equation x² − 273 = 0

Solution:

x² - 273 = 0 i.e. x² = 273
x = ±√273
Since the value of the square root of 273 is 16.523,
⇒ x = +√273 or -√273 = 16.523 or -16.523.
Example 2: If the surface area of a sphere is 1092π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1092π in²
⇒ r = ±√273 in
Since radius can't be negative,
⇒ r = √273
The square root of 273 is 16.523.
⇒ r = 16.523 in
Example 3: If the surface area of a cube is 1638 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 = 1638 in²
⇒ a = ±√273 in
Since length can't be negative,
⇒ a = √273
We know that the square root of 273 is 16.523.
⇒ a = 16.523 in

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FAQs on the Square Root of 273

What is the Value of the Square Root of 273?

The square root of 273 is 16.52271.

Why is the Square Root of 273 an Irrational Number?

Upon prime factorizing 273 i.e. 3¹ × 7¹ × 13¹, 3 is in odd power. Therefore, the square root of 273 is irrational.

Evaluate 20 plus 18 square root 273

The given expression is 20 + 18 √273. We know that the square root of 273 is 16.523. Therefore, 20 + 18 √273 = 20 + 18 × 16.523 = 20 + 297.409 = 317.409

What is the Square of the Square Root of 273?

The square of the square root of 273 is the number 273 itself i.e. (√273)² = (273)^2/2 = 273.

If the Square Root of 273 is 16.523. Find the Value of the Square Root of 2.73.

Let us represent √2.73 in p/q form i.e. √(273/100) = 2.73/10 = 1.652. Hence, the value of √2.73 = 1.652

What is the Square Root of -273?

The square root of -273 is an imaginary number. It can be written as √-273 = √-1 × √273 = i √273 = 16.522i
where i = √-1 and it is called the imaginary unit.

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