Square Root of 83

The square root of 83 is expressed as √83 in the radical form and as (83)^½ or (83)^0.5 in the exponent form. The square root of 83 rounded up to 6 decimal places is 9.110434. It is the positive solution of the equation x² = 83.

• Square Root of 83: 9.1104335791443
• Square Root of 83 in exponential form: (83)^½ or (83)^0.5
• Square Root of 83 in radical form: √83

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 83 can be written in multiple ways

• Radical form: √83 
• Decimal form: 9.11
• Exponent form: (83)^1/2

• 83 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
• Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 83 is an irrational number.

There are multiple ways to find the square root of 83-

• Long Division Method
• Estimation and Approximation

One can find out more about these methods by clicking here

Long Division Method

The square root of 83 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits 83 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
• Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 83. The number 9 fits here as 9 square gives 81. Dividing 83 by 9 with quotient as 9, we get the remainder as 2.
• Step 3: Drag a pair of 0’s down and fill it next to 2 to make the dividend 200.
• Step 4: Double the divisor 9, and enter 18 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 18X × X results in a value less than or equal to 200. This will be 1 in this case, so divide 200 with 181 and write the remainder. 
• Step 5: Repeat this process to get the decimal places you want.

Therefore, the square root of 83 = 9.11

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

• Step 1: Find a perfect square that is smaller than and bigger than 83. In this case, 9 and 10 will work as their squares are 81 and 100.
• Step 2: Writing in terms of inequality- 9<√83<10 = 81<83<100
• Step 3: Multiply by 100 and write in terms of square roots- √8100<√8300<√10000
• Step 4: Move closer to inequality- √8281<√8300<√8464 = 91<10√83<92
  = 9.1<√83<9.2
• Step 5: Taking average of upper and lower limits we get, (9.1 + 9.2)/2 = 9.15

Therefore, we can estimate the square root of 83 ≅ 9.15

Explore Square roots using illustrations and interactive examples

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• Square Root of 82
• Square Root of 85
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• Square Root of 81

• The square root of 83 is an irrational number.
• The number 83 is not a perfect square.
• There will be n/2 digits in the square root of an even number with n digits.
• There will be (n+2)/2 digits in the square root of an odd number with n digits.

• What is the square root of 83 up to 5 decimal places(Use Long Division)
• What are the roots of -83? Also, find the value of the square of the negative root of -83