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b the square root of 16 c √ 100 d the side length of a square that has an area of 49 cm2

Example 14 Evaluating squares and square roots

Now you try

Example 15

Locating square roots between whole numbers

State which consecutive whole numbers are either side of:

Now you try

State which consecutive whole numbers are either side of:

Example 16 Evaluating expressions involving squares and square roots

Now you try

Exercise 2G

PROBLEM-SOLVING a Explain why the floor length must be 8 tile lengths.

7 A square floor is covered with 64 square tiles.

7, 8 7–9 8–10 b Hence, find the perimeter of this floor in tile lengths. c If a square floor is covered with 81 square tiles, what would its perimeter be? a √ 72 b √ 83 c √ 26 d √ 34

8 The value of √ 19 as a decimal starts with 4 because √ 19 is between 4 and 5. Find the units digit for the following.

9 List all the square numbers between 101 and 200 (Hint: There are only four.)

10 a Find two square numbers that add to 85 b Find two square numbers that have a difference of 85.

REASONING

Squares and square roots are used by people who work with triangles, such as engineers, architects, builders, carpenters and designers. Electricians use a square root to calculate voltage: V = √ P × R , where P is power and R is resistance.

11

11 The value of 742 can be thought of as the area of a square with width 74 units. This square can be broken into few smaller areas as shown.

So 742 = 702 + 2 × 70 × 4 + 42

= 4900 + 560 + 16

= 5476 a 342 b 812 c 1032

Use a diagram like the one above to calculate these values.