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# Is 4.4721359549995794-2*sqrt(5)=0 ?

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Is 4.4721359549995794-2*sqrt(5)=0 ?

Guest Jun 20, 2017

#2
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4.4721359549995794 - 2√5  \(\stackrel{?}{=}\)  0

2*√5    is the same as    √20      so we can say...

4.4721359549995794 - √20  \(\stackrel{?}{=}\)  0

4.4721359549995794  \(\stackrel{?}{=}\)  √20

Square both sides.

(4.4721359549995794)^2  \(\stackrel{?}{=}\)  20

20.00000000000000006423465417690436  \(\stackrel{?}{=}\)   20

So we can see that it is very close, but not quite completely true.

Here is how I got the result on the last step.

Also, since  √20  is a non-terminating decimal,  there is no way that a terminating decimal can be equal to it.

hectictar  Jun 20, 2017
edited by hectictar  Jun 20, 2017
#1
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No not root 5 its root 20

Guest Jun 20, 2017
#2
+7324
+2

4.4721359549995794 - 2√5  \(\stackrel{?}{=}\)  0

2*√5    is the same as    √20      so we can say...

4.4721359549995794 - √20  \(\stackrel{?}{=}\)  0

4.4721359549995794  \(\stackrel{?}{=}\)  √20

Square both sides.

(4.4721359549995794)^2  \(\stackrel{?}{=}\)  20

20.00000000000000006423465417690436  \(\stackrel{?}{=}\)   20

So we can see that it is very close, but not quite completely true.

Here is how I got the result on the last step.

Also, since  √20  is a non-terminating decimal,  there is no way that a terminating decimal can be equal to it.

hectictar  Jun 20, 2017
edited by hectictar  Jun 20, 2017