Root Calculator | Best Calculator

Root Calculator

Result: 0
Formula:
x1/n = Result

Example:
If x = 16 and n = 2 (Square Root):
161/2 = 4
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In mathematics, the general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:

n√a = b
bn = a

Estimating a Root

Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Calculating square roots and nth roots is fairly intensive. It requires estimation and trial and error. There exist more precise and efficient ways to calculate square roots, but below is a method that does not require a significant understanding of more complicated math concepts. To calculate √a:

  1. Estimate a number b
  2. Divide a by b. If the number c returned is precise to the desired decimal place, stop.
  3. Average b and c and use the result as a new guess
  4. Repeat step two
EX:  Find √27 to 3 decimal places
 Guess: 5.125
27 ÷ 5.125 = 5.268
(5.125 + 5.268)/2 = 5.197
27 ÷ 5.197 = 5.195
(5.195 + 5.197)/2 = 5.196
27 ÷ 5.196 = 5.196

Estimating an nth Root

Calculating nth roots can be done using a similar method, with modifications to deal with n. While computing square roots entirely by hand is tedious. Estimating higher nth roots, even if using a calculator for intermediary steps, is significantly more tedious. For those with an understanding of series, refer here for a more mathematical algorithm for calculating nth roots. For a simpler, but less efficient method, continue to the following steps and example. To calculate n√a:

  1. Estimate a number b
  2. Divide a by bn-1. If the number c returned is precise to the desired decimal place, stop.
  3. Average: [b × (n-1) + c] / n
  4. Repeat step two
EX:  Find 8√15 to 3 decimal places
 Guess: 1.432
15 ÷ 1.4327 = 1.405
(1.432 × 7 + 1.405)/8 = 1.388
15 ÷ 1.3887 = 1.403
(1.403 × 7 + 1.388)/8 = 1.402

It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.

How to do square root on calculator?

1. Locate the Square Root Key:

  • Most scientific calculators have a dedicated square root key, which looks like this: “√”
     
  • Sometimes, it might be a secondary function, often above the “x²” key. In this case, you’ll need to press the “shift” or “2nd” key first.
     

2. Enter the Number:

  • Type in the number you want to find the square root of.

3. Press the Square Root Key:

  • Press the “√” key.
  • If it’s a secondary function, press “shift” or “2nd” and then the key with the square root symbol.
     

4. View the Result:

  • The calculator will display the square root of the number.

Example:

To find the square root of 25:

  1. Type “25”
  2. Press “√”
  3. The calculator will display “5”

Important Notes:

  • Negative Numbers: If you try to take the square root of a negative number on most basic calculators, you’ll get an error, as the result is an imaginary number. Some advanced calculators can handle complex numbers.  
     
  • Decimal Places: The calculator will usually display the result with several decimal places.

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