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Square Root of 314

The square root of 314 is expressed as √314 in the radical form and as (314)^½ or (314)^0.5 in the exponent form. The square root of 314 rounded up to 9 decimal places is 17.720045147. It is the positive solution of the equation x² = 314.

Square Root of 314: 17.72004514666935
Square Root of 314 in exponential form: (314)^½ or (314)^0.5
Square Root of 314 in radical form: √314

Square Root of 314

1.	What is the Square Root of 314?
2.	How to find the Square Root of 314?
3.	Is the Square Root of 314 Irrational?
4.	FAQs

What is the Square Root of 314?

The square root of 314, (or root 314), is the number which when multiplied by itself gives the product as 314. Therefore, the square root of 314 = √314 = 17.72004514666935.

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How to Find Square Root of 314?

Square Root of 314 by Long Division Method

Value of √314 by Long Division Method

Explanation:

Forming pairs: 03 and 14
Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
Bring down the next pair 14, to the right of the remainder 2. The new dividend is now 214.
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 7) such that 2Z × Z <= 214. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 214.
Divide 214 by 27 with the quotient as 7, giving the remainder = 214 - 27 × 7 = 214 - 189 = 25.
Now, let's find the decimal places after the quotient 17.
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. 7 + 27 = 34. To the right of 34, find a digit Z (which is 7) such that 34Z × Z <= 2500. Together they form a new divisor (347) for the new dividend (2500).
Divide 2500 by 347 with the quotient as 7, giving the remainder = 2500 - 347 × 7 = 2500 - 2429 = 71.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 314.

Therefore, the square root of 314 by long division method is 17.7 approx.

Is Square Root of 314 Irrational?

The actual value of √314 is undetermined. The value of √314 up to 25 decimal places is 17.72004514666935040199113. Hence, the square root of 314 is an irrational number.

☛ Also Check:

Square Root of 1521 - √1521 = 39
Square Root of 99 - √99 = 9.94987
Square Root of 45 - √45 = 6.70820
Square Root of 90 - √90 = 9.48683
Square Root of 49 - √49 = 7
Square Root of 320 - √320 = 17.88854
Square Root of 54 - √54 = 7.34847

Square Root of 314 Solved Examples

Example 1: Solve the equation x² − 314 = 0

Solution:

x² - 314 = 0 i.e. x² = 314
x = ±√314
Since the value of the square root of 314 is 17.720,
⇒ x = +√314 or -√314 = 17.720 or -17.720.
Example 2: If the surface area of a sphere is 1256π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1256π in²
⇒ r = ±√314 in
Since radius can't be negative,
⇒ r = √314
The square root of 314 is 17.720.
⇒ r = 17.720 in
Example 3: If the area of a circle is 314π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 314π in²
⇒ r = ±√314 in
Since radius can't be negative,
⇒ r = √314
The square root of 314 is 17.720.
⇒ r = 17.720 in

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FAQs on the Square Root of 314

What is the Value of the Square Root of 314?

The square root of 314 is 17.72004.

Why is the Square Root of 314 an Irrational Number?

Upon prime factorizing 314 i.e. 2¹ × 157¹, 2 is in odd power. Therefore, the square root of 314 is irrational.

What is the Square of the Square Root of 314?

The square of the square root of 314 is the number 314 itself i.e. (√314)² = (314)^2/2 = 314.

Is the number 314 a Perfect Square?

The prime factorization of 314 = 2¹ × 157¹. Here, the prime factor 2 is not in the pair. Therefore, 314 is not a perfect square.

What is the Square Root of 314 in Simplest Radical Form?

We need to express 314 as the product of its prime factors i.e. 314 = 2 × 157. Therefore, as visible, the radical form of the square root of 314 cannot be simplified further. Therefore, the simplest radical form of the square root of 314 can be written as √314

What is the Value of 2 square root 314?

The square root of 314 is 17.720. Therefore, 2 √314 = 2 × 17.720 = 35.440.

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