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

Guest Jun 20, 2017

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 #2
avatar+4747 
+2

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

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

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

Add     √20   to both sides.

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
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2+0 Answers

 #1
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0

No not root 5 its root 20

Guest Jun 20, 2017
 #2
avatar+4747 
+2
Best Answer

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

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

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

Add     √20   to both sides.

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

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