#NumberAndAlgebra #Path #Adv >[!info]- [Indices C (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa8d9baa84) >- MA5-IND-P-02 describes and performs operations with surds and fractional indices ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ---------------------------------- | --------------------------------- | ----------------------------------------- | | [[Fractions Decimals Percentages]] | - rational and irrational numbers | - identifying surds as irrational numbers | | [[Indices]] | - square roots and cube roots | - simplifying surds | | [[Algebraic Techniques B]] | - algebraic fractions | - rationalising the denominator | | [[Indices B]] | - negative indices | - fractional indices | ## [[Describe surds.pdf]] - Describe a real number as a number that can be represented by a point on the number line - Examine the differences between rational and irrational numbers and recognise that all rational and irrational numbers are real - Convert between recurring decimals and their fractional form using digital tools - Describe the term _surd_ as referring to irrational expressions of the form $\sqrt[n]{x}$ where $x$ is a rational number and $n$ is an integer such that $n$≥2, and $xgt;0 when $n$ is even - Recognise that a surd is an exact value that can be approximated by a rounded decimal - Demonstrate that $\sqrt{x}$ is undefined for $xlt;0 and that $\sqrt{x}$=0 when $x$=0 using digital tools - Describe $\sqrt{x}$ as the positive square root of $x$ for $xgt;0 and $\sqrt{0}$=0 ## [[Apply knowledge of surds to solve problems.pdf]] - Establish and apply the following results for $x>0$ and $y>0$: $\sqrt{x}^2=x=\sqrt{x^2}$, $\sqrt{xy}=\sqrt{x}\times\sqrt{y}$ and $\sqrt{\frac{x}{y}}=\frac{\sqrt{x}}{\sqrt{y}}$ - Apply the 4 operations to simplify expressions involving surds - Expand and simplify expressions involving surds - Rationalise the denominators of surds of the form $\frac{a\sqrt{b}}{c\sqrt{d}}$ ## [[Describe and use fractional indices.pdf]] - Apply index laws to describe fractional indices as: $a^{\frac{1}{n}}=\sqrt[n]{x}$ and $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$ - Translate expressions in surd form to expressions in index form and vice versa - Evaluate numerical expressions involving fractional indices including using digital tools