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Square Root of 274

The square root of 274 is expressed as √274 in the radical form and as (274)^½ or (274)^0.5 in the exponent form. The square root of 274 rounded up to 7 decimal places is 16.5529454. It is the positive solution of the equation x² = 274.

Square Root of 274: 16.55294535724685
Square Root of 274 in exponential form: (274)^½ or (274)^0.5
Square Root of 274 in radical form: √274

Square Root of 274

1.	What is the Square Root of 274?
2.	How to find the Square Root of 274?
3.	Is the Square Root of 274 Irrational?
4.	FAQs

What is the Square Root of 274?

The square root of 274, (or root 274), is the number which when multiplied by itself gives the product as 274. Therefore, the square root of 274 = √274 = 16.55294535724685.

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How to Find Square Root of 274?

Square Root of 274 by Long Division Method

Value of √274 by Long Division Method

Explanation:

Forming pairs: 02 and 74
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 74, to the right of the remainder 1. The new dividend is now 174.
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 <= 174. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 174.
Divide 174 by 26 with the quotient as 6, giving the remainder = 174 - 26 × 6 = 174 - 156 = 18.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 18. The new dividend is now 1800.
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 <= 1800. Together they form a new divisor (325) for the new dividend (1800).
Divide 1800 by 325 with the quotient as 5, giving the remainder = 1800 - 325 × 5 = 1800 - 1625 = 175.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 274.

Therefore, the square root of 274 by long division method is 16.5 approximately.

Is Square Root of 274 Irrational?

The actual value of √274 is undetermined. The value of √274 up to 25 decimal places is 16.55294535724684859324698. Hence, the square root of 274 is an irrational number.

☛ Also Check:

Square Root of 1024 - √1024 = 32
Square Root of 16 - √16 = 4
Square Root of 325 - √325 = 18.02776
Square Root of 200 - √200 = 14.14214
Square Root of 240 - √240 = 15.49193
Square Root of 74 - √74 = 8.60233
Square Root of 11 - √11 = 3.31662

Square Root of 274 Solved Examples

Example 1: Solve the equation x² − 274 = 0

Solution:

x² - 274 = 0 i.e. x² = 274
x = ±√274
Since the value of the square root of 274 is 16.553,
⇒ x = +√274 or -√274 = 16.553 or -16.553.
Example 2: If the surface area of a sphere is 1096π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1096π in²
⇒ r = ±√274 in
Since radius can't be negative,
⇒ r = √274
The square root of 274 is 16.553.
⇒ r = 16.553 in
Example 3: If the area of a circle is 274π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 274π in²
⇒ r = ±√274 in
Since radius can't be negative,
⇒ r = √274
The square root of 274 is 16.553.
⇒ r = 16.553 in

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FAQs on the Square Root of 274

What is the Value of the Square Root of 274?

The square root of 274 is 16.55294.

Why is the Square Root of 274 an Irrational Number?

Upon prime factorizing 274 i.e. 2¹ × 137¹, 2 is in odd power. Therefore, the square root of 274 is irrational.

What is the Square Root of -274?

The square root of -274 is an imaginary number. It can be written as √-274 = √-1 × √274 = i √274 = 16.552i
where i = √-1 and it is called the imaginary unit.

Evaluate 15 plus 3 square root 274

The given expression is 15 + 3 √274. We know that the square root of 274 is 16.553. Therefore, 15 + 3 √274 = 15 + 3 × 16.553 = 15 + 49.659 = 64.659

What is the Value of 17 square root 274?

The square root of 274 is 16.553. Therefore, 17 √274 = 17 × 16.553 = 281.400.

What is the Square Root of 274 in Simplest Radical Form?

We need to express 274 as the product of its prime factors i.e. 274 = 2 × 137. Therefore, as visible, the radical form of the square root of 274 cannot be simplified further. Therefore, the simplest radical form of the square root of 274 can be written as √274

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