Squares and Square Roots Mastery

Year 7 Mathematics Understanding exponents and square numbers Finding square roots up to 144

What is a Square Number?

A square number is formed when we multiply a number by itself Examples: 3 × 3 = 9, so 9 is a square number We can write this using exponents: 3² = 9 The small 2 is called an exponent or power

Square Numbers vs Regular Numbers

{"left":"Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144","right":"Regular numbers: 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15"}

Build the Squares

Using blocks or drawings, create visual squares for: 1² = 1 (1×1 square) 2² = 4 (2×2 square) 3² = 9 (3×3 square) 4² = 16 (4×4 square)

Using Exponent Notation

Instead of writing 5 × 5, we write 5² The base number is 5, the exponent is 2 Read as 'five squared' or 'five to the power of two' Examples: 6² = 36, 8² = 64, 10² = 100

Quick Check: Can You Find These?

What is 7²? What is 9²? What is 11²? What is 12²?

What is a Square Root?

A square root 'undoes' squaring If 8² = 64, then √64 = 8 The square root symbol is √ Square root asks: 'What number squared gives me this?'

Square Numbers and Their Roots Chart

Square Root Detective

Find the square root of these numbers: √25 = ? √49 = ? √100 = ? √121 = ?

Key Relationship

Squaring and finding square roots are inverse operations If a² = b, then √b = a This relationship helps us solve many mathematical problems