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# I don't know how to approach this...

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The question: please find the distance between the two points,

$$(1,\sqrt{2}) (5,\sqrt{8})$$

I don't know what my mistake was but here is how i approached this problem...
$$d=\sqrt{(-4)^2+(-2)^2} d= \sqrt{16+4} d=\sqrt{20} =2\sqrt{5}$$

Can someone please tell me how to solve this?

Jun 10, 2019

### 2+0 Answers

#1
+8077
+4

$$d\ =\ \sqrt{(1-5)^2+(\sqrt2-\sqrt8)^2}$$          But   $$\sqrt2-\sqrt8\ \neq\ -2$$    !!

$$d\ =\ \sqrt{(1-5)^2+(\sqrt2-2\sqrt2)^2}$$          because   $$\sqrt8\ =\ 2\sqrt{2}$$

$$d\ =\ \sqrt{(1-5)^2+(-\sqrt2\,)^2}$$          because   x - 2x  =  -x    so     $$\sqrt2-2\sqrt2\ =\ -\sqrt2$$

$$d\ =\ \sqrt{(-4)^2+(-\sqrt2\,)^2}$$          because  1 - 5  =  -4

$$d\ =\ \sqrt{16+2}$$          because   $$(-4)^2=16$$     and     $$(-\sqrt2)^2=2$$

$$d\ =\ \sqrt{18}$$

$$d\ =\ 3 \sqrt{2}$$_

Jun 10, 2019
#2
+30
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OHHHH, that makes so much more sense, thank you so much hectictar!! :)

Nirvana  Jun 10, 2019