11C

Index notation, squares and square roots

Writing repeated multiplication with index notation, evaluating powers, perfect squares and cubes, and square roots and cube roots.

Index notation

$3 \times 3 \times 3 \times 3 = 3^4 = 81$. Read $3^4$ as "3 to the power of 4". A number to the power $2$ is squared; to the power $3$ is cubed.

Square roots and cube roots

Squaring and square rooting

The square root undoes squaring. Drag P along the parabola.

Example 1●●

Between which two whole numbers does $\sqrt{40}$ lie?

$6^2 = 36$ and $7^2 = 49$.

$36 < 40 < 49$, so $6 < \sqrt{40} < 7$.

Flashcards

$2^5$

$32$

$sqrt{144}$

$12$

{27}$"]$3$

$sqrt{50}$ lies between

$7$ and $8$

Practice

Evaluate $3^4$.
Evaluate $\sqrt{49}$.
Evaluate $\sqrt[3]{64}$.
$\sqrt{40}$ lies between $6$ and which whole number?
Evaluate $2^5$.
Evaluate $5^3$.
$7 \times 7 \times 7$ in index notation is:
Evaluate $\sqrt{9} + \sqrt{196}$.