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 x² = 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

• If a = b², 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.

• 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.

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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• The square root of 313 can be written as √313.
• a × a = 313. It can also be written as: a² = 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.