Find a square root by the guess-and-check method (8th grade math)

I show how to find the square root of 34 to two decimal digits "manually" so to speak, without using the calculator's square root button. (We do use the calculator for multiplying.)

The basic idea is to make a guess, then multiply that guess by itself, and check how close to 34 we get.

I use a table to organize the work. We work with a low guess and a high guess iteratively, increasing the number of decimal digits, until we're sure what the value of square root of 34 is to two decimal digits.

See also

Irrational numbers — a video lesson

Math Mammoth Grade 8 curriculum

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