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NSW Y8 Maths Working with Numbers Power and Roots

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Power and Roots Theory

Numbers in the form \(a \times a \times a\) can be expressed in the form \(a^3\) where \(a\) is the base and \(3\) is the power or index. Similarly \(p^4\) can be expressed as \(p \times p \times p \times p\).\\ To find \(\sqrt{25}\) we need to find the same two numbers when multiplied together give 25.\\ \(\text { ie. } \sqrt{25}=\sqrt{5 \times 5}=5\)\\ In general \(\sqrt{a \times a}=\sqrt{a^2}=a\).\\ So the square root of perfect squares will give the number.\\ \begin{multicols}{2} \textbf{Example 1}\\ Solve \(3^2+2^3\) \\ \textbf{Example 1 solution}\\ $\begin{aligned} 3^2=3 \times 3 & =9 \\ 2^3=2 \times 2 \times 2 & =8 \\ \therefore 3^2+2^3 & =9+8 \\ & =17 \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ Find \(\sqrt{25 \times 9}\) \\ \textbf{Example 2 solution}\\ $\begin{aligned} \sqrt{25 \times 9} & =\sqrt{5 \times 5} \times \sqrt{3 \times 3} \\ & =5 \times 3 \\ & =15 \end{aligned}$\\ \textbf{Example 3}\\ Find \(\sqrt{25}+\sqrt{9}\)\\ \textbf{Example 3 solution}\\ $\begin{aligned} \sqrt{25}+\sqrt{9} & =\sqrt{5 \times 5}+\sqrt{3 \times 3} \\ & =5+3 \\ & =8 \end{aligned}$\\

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  • Power and Roots - Video - How to calculate the power of a number

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  • Power and Roots - Video - What are Square Roots? | Exponents | Best Square Root Tricks

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