Find the exact value... radicals.

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April 23rd 2012, 07:58 AM
modecasec

Find the exact value... radicals.

Having a hard time finding the answer to the problem. Can someone help me with this. (6-1)^2 + (15-3)^2 all of this is under a radical sign. I think the answer is 16.46. But I am not sure. I started out by squaring the two sets getting 36+1 +225+9 which equals 271 under a radical sign giving me the answer 16.46. Is this correct
April 23rd 2012, 08:23 AM
masters

Re: Find the exact value... radicals.

Quote:

Originally Posted by modecasec

Having a hard time finding the answer to the problem. Can someone help me with this. (6-1) + 15-3)2 all of this is under a ridical sign. I think the answer is 16.46. But I am not sure. I started out by squaring the two sets getting 36+1 +225+9 which equals 271 under a radical sign giving me the answer 16.46. Is this correct

Hi modecasec,

There's a problem with your notation. Your parentheses aren't balanced. You're missing one left parenthesis. Check you problem and edit your post.

What you have is $\sqrt{(6-1)+15-3)^2$ and that is incorrect.

It could be $\sqrt{((6-1)+(15-3))^2}=17$ , or

$\sqrt{(6-1)+(15-3)^2}=\sqrt{149}$ . I'm just guessing at what you intended, so edit your post.
April 23rd 2012, 08:26 AM
modecasec

Re: Find the exact value... radicals.

yes I messed that up. The two sets in parenthesis are raised to the secodn degree. what do you get now.
April 23rd 2012, 08:33 AM
Soroban

Re: Find the exact value... radicals.

Hello, modecasec!

It's hard to read what you typed, but I'll take a guess . . .

Quote:

$\sqrt{(6-1)^2 + (15-3)^2}$

First of all, be careful . . . Don't make up your own rules!
. . $(6-1)^2$ is not equal to $6^2+1^2$

Look at what we have:
. . $(6-1)^2 \:=\:5^2 \:=\:25$
. . $(15-3)^2 \:=\:12^2 \:=\: 144$

So we have: . $\sqrt{25 + 144} \:=\:\sqrt{169} \:=\:\boxed{13}$ . **

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

Another opportunity to make a fatal error . . .

. . $\sqrt{25 + 144}$ .is not equal to . $\sqrt{25} + \sqrt{144}$

Very tempting, isn't it? .Both 25 and 144 are squares.
Well, of course they are!
. . They just came from $5^2$ and $12^2$ , didn't they?

This tempting error appears every time we use the Pythagorean Theorem:
. . $a^2 + b^2 \:=\:c^2$
Think about it.