How do you find the principal square root of 8?



Answered question


How do you find the principal square root of 8?

Answer & Explanation

Jonathan Burroughs

Jonathan Burroughs

Beginner2021-12-30Added 37 answers

For a non-negative real number, n the principal square root is the non-negative solution to x2=n
The symbol n is used for the principal square root of n
The pricipal square root of 8, denoted 8 is the number whose sguare is 8. There is no easy method for finding this number. We use successive approximation (or other iterative techniques) to get increasingly accurate approximations.
We do, however write 8 in "simpler" form 22
8=42=42=22. Perhaps this is what you meant by "find"?
Travis Hicks

Travis Hicks

Beginner2021-12-31Added 29 answers

If, by "find" you mean get a decimal approximation, you could use: start with a number you know is close 32=9 and 22=4, so we'll start with 3 divide 8 by your last estimate: 8÷3=2.6667 (to 4 decimal places)
Average your previous estimate and the quotient: 3+2.66672=2.8334 (rounding)
Divide: 8÷2.8334=2.8235
Average: 2.8334+2.82352=2.8284
Divide: 8÷2.8284=2.8284
Average =2.8284
82.8284 this estimate is accurate to 4 decimal places.
If you need more accuracy, start again and keep more places when rounding.


Expert2022-01-08Added 777 answers

Thanks for the different answers.

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