Powers & Roots Flashcards

All 6 cards in this deck

What does $5^4$ mean?

$5\times5\times5\times5 = 625$.

What are the powers of 2 from $2^1$ to $2^{10}$?

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

True or false? $3^4 = 4^3$.

False. $3^4 = 81$ but $4^3 = 64$.

What does $\sqrt[n]{a}$ mean?

e.g. $\sqrt[3]{64}$

The number that gives $a$ when multiplied by itself $n$ times.
$\sqrt[3]{64}=4$, because $4\times4\times4=64$.

What are the steps to estimate the square root of a number that is not a square number?

e.g. estimate $\sqrt{78}$

1. Find the square numbers either side: $64 < 78 < 81$
2. So the root is between $8$ and $9$
3. $78$ is close to $81$, so $\sqrt{78}\approx 8.8$

True or false? Every positive number has two square roots, one positive and one negative.

True. e.g. $10^2 = 100$ and $(-10)^2 = 100$, so the square roots of 100 are $10$ and $-10$.