# Video: Pack 2 β’ Paper 1 β’ Question 15

Pack 2 β’ Paper 1 β’ Question 15

02:37

### Video Transcript

Make π‘ the subject of the formula π  equals the cube root of five over π‘ squared plus four.

So the key thing about this question is that π‘ is what weβre trying to make the subject of the formula. Okay, so weβve got π  is equal to the cube root of five over π‘ squared plus four. So therefore, the first step is to actually subtract four from each side. So we get π  minus four is equal to the cube root of five over π‘ squared.

Then, next, what we actually want to do is the inverse of the cube root because we got the cube root of five over π‘ squared. And to actually enable us to do that, what weβre gonna do is actually cube both sides of our equation, which is gonna give us π  minus four all cubed is equal to five over π‘ squared.

And then, what weβre gonna do is actually multiply each side of the equation by π‘ squared cause we actually got that down as the denominator. We donβt want it as a denominator. So weβre gonna multiply each side by π‘ squared. So we get π‘ squared multiplied by π  minus four all cubed equals five.

Then, at this stage, we remind ourselves that itβs π‘ that we want as the subject to the formula. So what weβre actually gonna do is divide through by π  minus four all cubed. So weβre gonna have π‘ squared is equal to five over π  minus four all cubed. So now, as weβre looking for single π‘ as a subject to the formula, what weβre gonna do is actually square root each side because itβs the inverse of squared because we have π‘ squared.

So now, for this next step, what weβre actually gonna do is use a little rule we know. And thatβs the root of π over π is actually equal to the root of π divided by the root of π. So using this rule, weβre gonna get π‘ is equal to root five over root and then π  minus four all cubed.

So now, what weβre gonna do is actually use one of our index rules to actually simplify this further because we know that the πth root of π₯ is equal to one over π. So therefore, we can actually rewrite this as π‘ is equal to root five over and then weβve got π  minus four to the power of three then this all to the power of a half.

And then, we can actually use one more index law to just help us get to our final solution. And that index law is that π₯ to the power of π to the power of π is equal to π₯ to the power of ππ. So we actually multiply the powers. So therefore, we can say that if we make π‘ the subject to the formula π  equals the cube root of five over π‘ squared plus four, we get π‘ equals root five over π  minus four to the power of three over two.

And we got that last bit because we had π  minus four to the power of three to the power of a half. Then, we actually used the index law, multiplied them together. And three multiplied by a half gives us three over two.