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Square Root of 313
The square root of 313 is expressed as √313 in the radical form and as (313)^{½} or (313)^{0.5} in the exponent form. The square root of 313 rounded up to 9 decimal places is 17.691806013. It is the positive solution of the equation x^{2} = 313.
 Square Root of 313: 17.69180601295413
 Square Root of 313 in exponential form: (313)^{½} or (313)^{0.5}
 Square Root of 313 in radical form: √313
1.  What Is the Square Root of 313? 
2.  Is Square Root of 313 Rational or Irrational? 
3.  How to Find the Square Root of 313? 
4.  Important Notes 
5.  FAQs on Square Root of 313 
What Is the Square Root of 313?
 If a = b^{2}, then √a = b, where a and b are natural numbers. √a is the square root of a and it is expressed in the exponential form as a^{½}.
 √313 = √(a number × a number)
 √313 = (17.69180 × 17.69180) or ( 17.69180 × 17.69180) ⇒ √313 = ±17.69180.
Is Square Root of 313 Rational or Irrational?
 313 is not a perfect square, which means that it does not have a natural number as its square root.
 Square root of 313 in the decimal form is √313 = ±17.69180.
 Square root of 313 cannot be expressed as a fraction of the form p/q. This indicates that the square root of 313 is an irrational number.
How to Find the Square Root of 313?
There are two ways to find the square root of 313:
 Long Division Method
 Prime Factorization Method
Long Division Method
The square root of 313 by long division method consists of the following steps:
 Step 1: Write 313.000000. Take the number in pairs from the right. 1 stands alone. Now divide 3 by a number such that (number × number) gives ≤ 3. Obtain quotient = 1 and remainder = 1. Double the quotient. We get 2. Have 27 as our new divisor. Bring down 13 for division.
 Step 2: Find a number such that (2 + that number) × that number gives the product ≤ 2 13. We find that 27 × 7 = 189 . Subtract from 2 13 and get 24 as the remainder. Bring down the pair of zeros. 24 00 is our new divisor.
 Step 3: 17 is our quotient and on doubling it becomes 34 and 2400 is our new divisor. Find a number such that number gets 24 00 or less than that. We find 346 × 6 = 2076. Subtract this from 24 00  20 76 and get the remainder and bring down the zeros.3 24 00 becomes the new dividend. Repeat the steps until we approximate the square root to 3 decimal places. We get, √313 = 17.691.
Therefore, the square root of 313 = 17.691.
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Important Notes:
 The square root of 313 can be written as √313.
 a × a = 313. It can also be written as: a^{2} = 313.
 a = √313, a is the 2^{nd} root of 313 and a = 17.691.
 The square root of any number has two values; one is positive and the other is negative. So, √313 = +17.691 or  17.691.
 In the exponential form, we denote √313 as (313) ^{½}.
 In the simplest radical form square root of 313 is written as √313.
Square Root of 313 Solved Examples

Example 1: Jack is multiplying a number by itself. If the product is 313, help Jack find the number.
Solution:
To find the number, let us assume the number to be z
On multiplying z times z = z × z = 313
z² = 313
z = √313
z = 17.691
(17.691 × 17.691 = 312.971 ≅ 313)
The number is 17.691. 
Example 2: The area of a squareshaped garden is 97,969 square units. Calculate the length of one side of the garden.
Solution:
The area of the garden = 97,969 sq. units. To find the side of a squareshaped garden, let us take square root of 97,969 by prime factorization method.
√97,969 = (313 × 313) = 313
Square root of 97,969 is 313. Therefore, the length of the side of the square mat is 313 units. 
Example 3: What number should Jack subtract from 313 to obtain a perfect square?
Solution:
Square root of 313 lies between 17 and 18. The square root of 17 is 289. On subtracting 24 from 313 we gt 289. 289 is a perfect square. The number is 24.
FAQs on the Square Root of 313
What is the Value of the Square Root of 313?
The square root of 313 is 17.6918.
Why is the Square Root of 313 an Irrational Number?
The number 313 is prime. This implies that the number 313 is pairless and is not in the power of 2. Therefore, the square root of 313 is irrational.
Is the number 313 a Perfect Square?
The number 313 is prime. This implies that the square root of 313 cannot be expressed as a product of two equal integers. Therefore, the number 313 is not a perfect square.
What is the Square Root of 313 in Simplest Radical Form?
The number 313 is a prime number. This implies that the number 313 is pairless and is not in the power of 2. Therefore, the radical form of square root of 313 cannot be simplified further.
If the Square Root of 313 is 17.692. Find the Value of the Square Root of 3.13.
Let us represent √3.13 in p/q form i.e. √(313/100) = 3.13/10 = 1.769. Hence, the value of √3.13 = 1.769
What is the Square Root of 313?
The square root of 313 is an imaginary number. It can be written as √313 = √1 × √313 = i √313 = 17.691i
where i = √1 and it is called the imaginary unit.
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