Write down all the irrational numbers. 22/7, $\dfrac{\sqrt{2}}{2}$, $\sqrt[3]{-8}$, $\pi$, -0.3 Answer ... Calculate $\dfrac{4.23^{3} - 3.4 + 2}{\sqrt{41.35}}$ and write down your answer correct to 1 significant figure. Answer ...

1. Identify which listed numbers are irrational

$\dfrac{22}{7}$ is rational since it is a fraction of integers.

$\dfrac{\sqrt{2}}{2}$ is irrational since $\sqrt{2}$ is irrational, and dividing by $2$ keeps it irrational.

$\sqrt[3]{-8}=-2$, so it is rational.

$\pi$ is irrational.

$-0.3$ is rational since it is a terminating decimal.

1. Evaluate the expression using a calculator

$\frac{4.23^{3}-3.4+2}{\sqrt{41.35}}=\frac{74.286067}{\sqrt{41.35}}\approx 11.552\ldots$

2. Round the calculator value to 1 significant figure

$11.552\ldots \approx 10 \quad \text{correct to 1 significant figure}$