Maths Help: How to Change the Subject of an Equation or Formula

Uploaded by vividmaths on 15.03.2012

Ok this is a most empowering example for moving around and getting the new subject. At the
moment we have a little “a” equals big square root of A over B now what we're trying
to do here is get B as the subject so we’ve marked it up.
First thing we do was marked up want we want as the subject. So little “a” is the subject
now how do we make capital B the subject? Can we swap them? Not that easy. Let me show
you what to do.Since the right hand side is square rooted, the left isn’t; let’s remember
with equations, let’s do what we do on the one side the same thing to the other side.
So to get rid of the square root, what do we do? We need to square root don’t we so
let’s square: put brackets here so we let’s square these sides and now when you square
this side you also have to square that side don’t we? Just to balance things. So squaring
a square root basically nullifies itself and it stays the same because when you square
a square root, it’s like adding one and you subtract it when you're back in the same
place. So that is becoming quite simply A on B ok. Now on this side we’ve got the
A squared – how do we make B the subject? That’s the question now. So well that’s
the denominator so let’s multiply both sides by B that may help so multiply by B, multiply
by B. Now other here in the right hand side, multiplying by B and the denominator will
cancel it so cancel, cancel – and we're left with the A over here. And on the left
hand side it simply A squared B – equals A and now we still need to make B to be subject
so how we are going to do to remove the A squared? That’s right, let’s divide by
A squared divide by A squared so it's quite simple to leave the B to divide itself. B
equals capital A all over little “a” all squared. That is your subject.
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