# KS3. Number. 3. Squares, cubes, roots & indices

Square Numbers

Every number has a square number. We find it by multiplying the number by itself.

Which ones have you already memorised? why not try to memorise a few more?

Square roots

A square root of a number is the number that it is the square of,  eg. 169 has 13 as a square root.

BUT

Every positive number has two square roots, a positive one and a negative one. Why is this so?

The √ sign only refers to the positive square root, not to the negative one

ALSO

Don’t forget the geometrical meaning of a square number and a square root!

Practice Question Set 1. (from exercise 1F on page 14 of the year 8 textbook)

Answers to Practice Question Set 1

1. a. 81, b. -11, 11, c. 196, d. 0, e. 169, f. -8, 8
2. a. 12.96, b. -4.1, 4.1, c. 0.1024, d. -0.4, 0.4, e. 129.96, f. -0.8, -.8
3. a. 1.2769, b. -2.5, 2.5, c. 9.71, d. -1,58, 1.58
4. a. 2.8cm, b. 7.8m, c. 12.5mm
5. a. 10.4m2, b. 47.61mm2, c. 2.89cm2
6. a. 4/7, b. 9/10, c. 5/8
7. a. 6/10 = 3/5, b. 9/10, c. 12/10 =6/5
8. √(64/100)

Cubes & Cube Roots

The cube of 6 is 6x6x6 (can you work it out in your head?)

What is the cube root of 125?  Is there just one cube root? Or two? Or three?

What is the geometrical representation of cubes and cube roots?

ALSO

Can a negative number have a cube root?

What is the biggest number that you can cube “in your head”?  Why not memorise 2 more?

Practice Question Set 2 (from exercise 1G on page 15 of the year 8 textbook)

Answers to Practice Question Set 2

Index Notation

What does 26 mean?

What does (-2)6 mean?

What does -26 mean?

Practice Question Set 3 (from exercise 1H on page 16 of the year 8 textbook)

Answers to Practice Question Set 3