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

[Einstein's Cat]

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.

 

[ProfuselyQuarky]

What's the opposite of a square root?

 

[Ssnow]

you can start doing the square of your equation (both side), so $C^{2}=a^{2}+b^{2}$.

 

[ProfuselyQuarky]

you can start doing the square of your equation (both side), so $C^{2}=a^{2}+b^{2}$.

The OP was supposed to answer

 

[Ssnow]

Only an input ... , now it is your turn ...

 

[ProfuselyQuarky]

$C^2=a^2+b^2$
$b^2=C^2-a^2$

Now, @Einstein's Cat what's the last step?

 

[symbolipoint]

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]

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

 

[Einstein's Cat]

Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives

 

[ProfuselyQuarky]

Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives

No prob! It was amusing.

 

[symbolipoint]

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.

Aw, you knew what he/she meant

Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives

No prob! It was amusing.

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).

 

[SteamKing]

Jesus! I just realized how stupid my question was; numerous apologies for diminishing your lives

It's OK. You're only a Cat.

 

[Mark44]

you can start doing the square of your equation (both side), so $C^{2}=a^{2}+b^{2}$.

$C^2=a^2+b^2$
$b^2=C^2-a^2$

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.

 

[micromass]

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.

 

[ProfuselyQuarky]

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! :(

 

[Einstein's Cat]

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.

 

[micromass]

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?

 

[Einstein's Cat]

What is your solution?

The square root of c^2 - a^2

 

[micromass]

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: $\sqrt{b^2} \neq b$.

 

[ProfuselyQuarky]

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

 

[Einstein's Cat]

I

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

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.

 

[micromass]

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!

 

[berkeman]

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.

 

[symbolipoint]

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.

Hey! I agree with micromass about this.

 

[Mark44]

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.

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.

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.

 

[Einstein's Cat]

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

 

[Samy_A]

$5=\sqrt{3²+( -4 )^2}$

 

[Mark44]

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.

 

[Einstein's Cat]

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.

 

[ProfuselyQuarky]

Sorry about that! I meant "incomplete" but typed otherwise and I now understand.

So you know what the answer is now?