# Approximate of square root of 2

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• Oct 25th 2010, 12:26 PM
Natasha1
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?
• Oct 25th 2010, 12:39 PM
mr fantastic
Quote:

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 ....
• Oct 25th 2010, 12:41 PM
HappyJoe
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, 12:44 PM
Natasha1
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, 01:40 PM
Archie Meade
$\displaystyle\frac{63}{45}=\frac{(9)7}{(9)5}=\frac {7}{5}=1\frac{2}{5}=1.4$

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