Surds

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Conversions between index and surd forms

Lesson

Consider the following.

Rewrite $x^{\frac{1}{3}}$

`x`13 in surd form.Evaluate $\sqrt[3]{x}$

^{3}√`x`for when $x=125$`x`=125.

Complete the blank to make the statement true.

$10^{\frac{1}{3}}=\sqrt[3]{\editable{}}$1013=

^{3}√

Fill in the blanks to simplify the given expression.

$\sqrt{m^8}$√ `m`8$=$= $\left(m^8\right)^{\editable{}}$( `m`8)$=$= $m^{\editable{}\times\frac{1}{2}}$ `m`×12$=$= $m^{\editable{}}$ `m`

Manipulate complex numbers and present them graphically

Apply the algebra of complex numbers in solving problems