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?

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- Oct 25th 2010, 11:26 AMNatasha1Approximate 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? - Oct 25th 2010, 11:39 AMmr fantastic
- Oct 25th 2010, 11:41 AMHappyJoe
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.

- Oct 25th 2010, 11:44 AMNatasha1
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 - Oct 25th 2010, 12:40 PMArchie Meade
$\displaystyle \displaystyle\frac{63}{45}=\frac{(9)7}{(9)5}=\frac {7}{5}=1\frac{2}{5}=1.4$

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