Thread: Approximate of square root of 2

62/45 < square root of 2 < 64/45

Use these bounds to write the value of square root of 2 to an appropriate degree of accuracy?

Originally Posted by Natasha1

62/45 < square root of 2 < 64/45

Use these bounds to write the value of square root of 2 to an appropriate degree of accuracy?

Perhaps 63/45 and long division ....

I'm not sure about the depth of this question. For starters, a reasonable approximation of sqrt(2) given those two inequalities would be the average of the bounds. In other words, try calculating the average of 62/45 and 64/45, and see how well this value serves as an approximation of the square root of 2.

I'm asking this because I don't understand how to go about answering a question like this one. Never done it before...

Would it be wise to then write something like this

62/45 = 1.377777777....
64/45 = 1.422222222....
and 63/45 = 1.4

so square root of 2 is approximately 1.4

which is maybe the idea, so yes it's a "reasonable" approximation.