What you need to know

Things to remember:

• It is easier to learn some of the basic cube roots instead of trying to find them each time.

Although we’re going to be looking at cube rooting, it is best to start refreshing on an easier topic, squaring and square rooting.

Squaring just means multiplying a number by itself:

$$5^2=5\times5=25$$

$$9^2=9\times9=81$$

$$11^2=11\times11=121$$

Square rooting tells us what number we multiply by itself to make our original number.

$$\sqrt{25}=5$$

$$\sqrt{81}=9$$

$$\sqrt{121}=11$$

We have seen cubing before, this is just the “mathy” word for “power of 3”

$$4^3=4\times4\times4=64$$

$$7^3=7\times7\times7=343$$

$$10^3=10\times10\times10=1000$$

So, if square rooting tells us what we multiply by itself to find our number, what do you think cube rooting might be?… Cube rooting just tells us what we multiply by itself twice to make our starting number. We write this like a square root, but with a little 3 on the left.

$$\sqrt[3]{64}=4$$

$$\sqrt[3]{343}=8$$

$$\sqrt[3]{1000}=10$$

Finding cube roots can be difficult, so it can be helpful to learn the first 10.

Number                       Cube Root

1                                  1

8                                  2

27                                3

64                                4

125                              5

216                              6

343                              7

512                              8

729                              9

1000                            10

Example Questions

Question 1: What is the cube root of 343?

Answer

$$\sqrt[3]{343}=7$$

Question 2: What is the cube root of 729?

Answer

$$\sqrt[3]{729}=9$$