Rearranging formulae

More advanced techniques are required to rearrange any formulae that involve any powers or roots. Further techniques are needed if the variable which needs to be the subject appears twice.

Example

Rearrange the formula \(T = 2 \pi \sqrt{\frac{L}{G}}\) to make \(L\) the subject.

If a formula contains a power or a root then this must be isolated before performing the inverse operation.

Firstly, isolate the root:

\(\begin{array}{ccc} T & = & 2 \pi \sqrt{\frac{L}{G}} \\ \div 2 \pi && \div 2 \pi \end{array}\)

\(\frac{T}{2 \pi} = \sqrt{\frac{L}{G}}\)

Now 'square' both sides:

\(\left(\frac{T}{2 \pi}\right)^2 = \left(\sqrt{\frac{L}{G}}\right)^2\)

Lastly, multiply by \(G\):

\(\begin{array}{ccc} \left(\frac{T}{2 \pi}\right)^2 & = & \frac{L}{G} \\ \times G && \times G \end{array}\)

\(G \left(\frac{T}{2 \pi}\right)^2 = L\)

Question

The formula for the surface area, \(A\), of a closed box is given by:

\(A = 2wb + 2wh + 2bh\)

Rearrange this formula to make \(b\) the subject.

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Algebraic formulae - EduqasRearranging formulae