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Square Root Of 3

The root of three is expressed as √3 within the radical type and as (3)½ or (3)0.5 within the exponent type. If the square root of 3 rounded up to 7 decimal places is 1.7320508.  

  • Square Root of 3: 1.7320508075688772
  • Square Root of 3 in exponential form: (3)½ or (3)0.5
  • Square Root of 3 in radical form: √3

Square Root Of 3

If a number that when multiplied by itself, results in the original number then it’s said to be the square root of the given number. 

For instance, the square root of 16 is 4, as 4 times 4 results in16. 

There are square roots of some numbers that do not result in whole numbers, such as 3. 

We can categorise the root of three in numerous ways that                    

  •                 Decimal form= 1.732.
  • Radical form=  √3
  • Exponent form=  31/2

Can the square root of 3 be considered a rational or an irrational number?

  • The decimal part of square root 3 is non-terminating. 
  • √3 = 1.732050807……. Is a never-ending decimal.
  • Hence, the square root of 3 is an irrational number.

Finding the Square Root of 3?

The square root of 3 is never-ending and in such case, the long-division method is used to calculate its value. 

  • Step1: To begin, we write 3 as 3.000000, then from left to right, we group the 0s after the decimal point in pairs of two. 
  • Step 2: Conjure up a number that is less than or equal to 3 when multiplied by itself. That number would be 1 in this scenario.
  • Step 3: We get a remainder of 2 by dividing 3 by 1 with a quotient of 1.
  • Step 4: To make the dividend 200, drag a pair of 0s down and place them next to 2.
  •         Step 5: Divisor 1 is multiplied by itself, and the result is written below. We now have 2X as the new divisor, and we must find a number for X such that the product of 2X X is less than or equal to 200. The needed value is 27 in this case.
  •     Step 6: After a decimal place, the number 7 is added to the quotient. The subsequent division’s new divisor will be 2X + X, which in this case is 34.

We may calculate the rest of the decimals by repeating step 4 in the same manner.


  • The real roots of √3 are ± 1.732.
  • The Square root of other numbers is always irrational and a perfect square will always be rational. For example, √25 = 5, whereas √17 = 4.1231…

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