Solving for b in C = sqrt(a^2 + b^2)

  • B
  • Thread starter Einstein's Cat
  • Start date
In summary: Can you give me an example of a number that is equal to its square root? (more than one).Also, I am struggling with the concept of how root b^2 is not equal to bThe square root function is the inverse of the squaring function, which means that it “undoes” the squaring operation. So, if you square a number (e.g. 5), and then apply the square root function, you get back to the original number (i.e. 5). However, not all numbers have this property. For example, the number 4 is the square of 2, so if you square root 4, you get 2. But the number -4 is NOT the
  • #1
Einstein's Cat
182
2
Say if
C = square root (a^2 + b^2),
How could one make the term "b" the subject of the equation? Thank you for your help.
 
Mathematics news on Phys.org
  • #2
What's the opposite of a square root?
 
  • Like
Likes Ssnow
  • #3
you can start doing the square of your equation (both side), so ##C^{2}=a^{2}+b^{2}##.
 
  • #4
Ssnow said:
you can start doing the square of your equation (both side), so ##C^{2}=a^{2}+b^{2}##.
The OP was supposed to answer :smile:
 
  • #5
Only an input ... , now it is your turn ... :wink:
 
  • Like
Likes ProfuselyQuarky
  • #6
##C^2=a^2+b^2##
##b^2=C^2-a^2##

Now, @Einstein's Cat what's the last step?
 
  • #7
Let me play dim-witted for a few seconds:
There is a variable and an expression and these are related by equality. How would any of that be or have a "subject"?

Now let me play as if I know what is really wanted:
Just use INVERSE operations to undo what has been done to b, so you solve the equation for b, to have a formula to show what is an expression for b.
 
  • #8
symbolipoint said:
Let me play dim-witted for a few seconds:
There is a variable and an expression and these are related by equality. How would any of that be or have a "subject"?
Aw, you knew what he/she meant :cool:
 
  • #9
Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives
 
  • Like
Likes ProfuselyQuarky
  • #10
Einstein's Cat said:
Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives
No prob! It was amusing. :-p
 
  • #11
symbolipoint said:
Let me play dim-witted for a few seconds:
There is a variable and an expression and these are related by equality. How would any of that be or have a "subject"?

Now let me play as if I know what is really wanted:
Just use INVERSE operations to undo what has been done to b, so you solve the equation for b, to have a formula to show what is an expression for b.
ProfuselyQuarky said:
Aw, you knew what he/she meant :cool:
Einstein's Cat said:
Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives
ProfuselyQuarky said:
No prob! It was amusing. :-p
Maybe I should not have said the way I did say.
The way "subject" is used seems to expect that the equation is a sentence and works according to the grammar of the language, but such is for HUMAN languages, and not for an extremely precise written language such as "Algebra". According to that, treating a number within an equation as any element of a sentence or as any part of speech part of sentence structure seems out-of-place; but still the question YOU ask suggests that you want to solve the equation for b, and to have a formula for b. Maybe this is a cultural thing; or maybe I have not seen a few new trends in mathematics education - I thought I would have seen this already if it were a normal way of discussing (subject, as part of numbers in an equation).
 
  • Like
Likes ProfuselyQuarky
  • #12
Einstein's Cat said:
Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives
It's OK. You're only a Cat.
 
  • Like
Likes ProfuselyQuarky and DrewD
  • #13
Ssnow said:
you can start doing the square of your equation (both side), so ##C^{2}=a^{2}+b^{2}##.

ProfuselyQuarky said:
##C^2=a^2+b^2##
##b^2=C^2-a^2##

Now, @Einstein's Cat what's the last step?
If the OP hadn't already seen these posts I would have deleted them. Giving too much help is a violation of the rules of this forum.
 
  • Like
Likes ProfuselyQuarky
  • #14
Einstein's Cat said:
Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives

Can you post what you think is the solution. It is very likely that what you think is incorrect.
 
  • Like
Likes epenguin
  • #15
Mark44 said:
If the OP hadn't already seen these posts I would have deleted them. Giving too much help is a violation of the rules of this forum.
Sorry! :(
 
  • #16
micromass said:
Can you post what you think is the solution. It is very likely that what you think is incorrect.
Denouncing the mathematical abilities of others is obscenely unnecessary and by doing so, your personal interpretation of the extent of your ability is not enhanced. Thus, I advise you cease denouncing other's abilities and instead designate time to advancing your own.
 
  • #17
Einstein's Cat said:
Denouncing the mathematical abilities of others is obscenely unnecessary and by doing so, your personal interpretation of the extent of your ability is not enhanced. Thus, I advise you cease denouncing other's abilities and instead designate time to advancing your own.

What is your solution?
 
  • #18
micromass said:
What is your solution?
The square root of c^2 - a^2
 
  • #19
Einstein's Cat said:
The square root of c^2 - a^2

Exactly like I thought. That is the wrong solution. This is why I asked. Instead of berating me for being arrogant, you should trust my skills in knowing when a student like has a flaw in his/her thinking! I rarely go wrong there.

To give a hint where you go wrong: ##\sqrt{b^2} \neq b##.
 
  • Like
Likes epenguin and DrewD
  • #20
Mmm… @Einstein's Cat even if you’re personally annoyed with @micromass for showing how you are wrong, it would only benefit yourself to try at it again :smile:
 
  • #21
I
ProfuselyQuarky said:
Mmm… @Einstein's Cat even if you’re personally annoyed with @micromass for showing how you are wrong, it would only benefit yourself to try at it again :smile:
I would like to clarify that I very much appreciate the provided help, it is however the dismissive attitude that was adopted that irritated me. Also, I am struggling with the concept of how root b^2 is not equal to b. Once again any help would be appreciated.
 
  • #22
Einstein's Cat said:
I

I would like to clarify that I very much appreciate the provided help, it is however the dismissive attitude that was adopted that irritated me. Also, I am struggling with the concept of how root b^2 is not equal to b. Once again any help would be appreciated.

You should be happy I posted, otherwise you would have a wrong solution and you would not have learned something new! Dislike me all you want, but I did provide you valuable help!
 
  • Like
Likes ProfuselyQuarky and berkeman
  • #23
Einstein's Cat said:
Also, I am struggling with the concept of how root b^2 is not equal to b
It's equal to more than just "b". Think for a bit and work some examples... I bet you can figure it out. :smile:
 
  • #24
micromass said:
Can you post what you think is the solution. It is very likely that what you think is incorrect.
Einstein's Cat said:
Denouncing the mathematical abilities of others is obscenely unnecessary and by doing so, your personal interpretation of the extent of your ability is not enhanced. Thus, I advise you cease denouncing other's abilities and instead designate time to advancing your own.
Hey! I agree with micromass about this.
 
  • #25
micromass said:
Can you post what you think is the solution. It is very likely that what you think is incorrect.

Einstein's Cat said:
Denouncing the mathematical abilities of others is obscenely unnecessary and by doing so, your personal interpretation of the extent of your ability is not enhanced. Thus, I advise you cease denouncing other's abilities and instead designate time to advancing your own.
We get a lot of people who misunderstand square roots. micromass was extrapolating from a very large sample to make a prediction about your answer.
Einstein's Cat said:
The square root of c^2 - a^2
As an equation, that would be ##b = \sqrt{c^2 - a^2}##. It's not wrong, per se, but it is incomplete.
 
  • Like
Likes ProfuselyQuarky
  • #26
Mark44 said:
We get a lot of people who misunderstand square roots. micromass was extrapolating from a very large sample to make a prediction about your answer.

As an equation, that would be ##b = \sqrt{c^2 - a^2}##. It's not wrong, per se, but it is incomplete.
May I inquire why it is complete
 
  • #27
##5=\sqrt{3²+( -4 )^2}##
 
Last edited:
  • #28
Einstein's Cat said:
May I inquire why it is complete
What I said was that your solution was incomplete, the opposite of complete. There are two solutions to the equation, not the one that you showed.
 
  • #29
Mark44 said:
What I said was that your solution was incomplete, the opposite of complete. There are two solutions to the equation, not the one that you showed.
Sorry about that! I meant "incomplete" but typed otherwise and I now understand.
 
  • #30
Einstein's Cat said:
Sorry about that! I meant "incomplete" but typed otherwise and I now understand.
So you know what the answer is now?
 
  • #31
ProfuselyQuarky said:
So you know what the answer is now?
B= square root( +/- c^2 - +/- a^2) I believe
 
  • #32
Einstein's Cat said:
B= square root( +/- c^2 - +/- a^2) I believe
Still an incomplete answer ...

As ##(-c)²=(+c)²##, this answer is not different from your previous one.
 
  • Like
Likes ProfuselyQuarky
  • #33
Try again. You can do it!
 
  • #34
##\sqrt {c^2-a^2}## has two answers. Think how the same equation (with a square root) can have two solutions.
 
Last edited:
  • #35
ProfuselyQuarky said:
##\sqrt {c^2-a^2}## has two answers. Think how the same equation (with a square root) can have two solution.
Hmm, I'm not sure this is totally correct (although I know what you mean).

By convention, ##\sqrt a## represents the positive square root of ##a##, where ##a## is a non negative real number.
 
  • Like
Likes ProfuselyQuarky

Similar threads

B Complete the square, yes, but what does it mean?
Replies
19
Views
2K
I Trouble Solving an Equation that has square roots on both sides
Replies
1
Views
1K
B Can Higher Degree Nested Radicals Be Simplified?
2
Replies
41
Views
1K
MHB Finding $b(a+c)$ for Real Roots of $\sqrt{2014}x^3-4029x^2+2=0$
Replies
1
Views
999
MHB What is the value of $(a+c)(b+c)(a-d)(b-d)$ given specific roots?
Replies
6
Views
1K
B Principal square root of a complex number, why is it unique?
Replies
13
Views
4K
MHB Triangle Equality Proof: $\frac{a}{b}=1+\sqrt{2\left(\frac{c}{b}\right)^2-1}$
Replies
1
Views
1K
B What went wrong with (-x)^2=x^2?
Replies
22
Views
1K
MHB Prove Triangle Inequality: $\sqrt{2}\sin A-2\sin B+\sin C=0$
Replies
2
Views
1K
MHB Prove $a^2+b^2-c^2>6(c-a)(c-b) for $a^3+b^3=c^3$
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top