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Middle Years

1.05 Square roots and perfect squares

Worksheet
Perfect squares
1

State whether the following numbers are perfect squares:

a
6
b
25
c
49
d
44
e
18
f
144
g
36
h
12
2

Evaluate the following:

a
4^{2}
b
7^{2}
c
9^{2}
d
12^{2}
e
9^{2} + 6
f
3^{2} + 7^{2}
g
7^{2} + 9^{2}
h
100^{2} + 10^{2}
i
7^{2} - 3^{2}
j
9^{2} - 8^{2}
k
12^{2} - 6^{2}
l
100^{2} - 10^{2}
3

Harry was working out 2^{2} \times 5^{2} and thought that he could simplify the expression using the fact that 2 \times 5 = 10.

a

Evaluate 2^{2} \times 5^{2}, by first expanding and evaluating each square.

b

Now, using the fact 2 \times 5 = 10, evaluate 10^{2}.

c

Is 2^{2} \times 5^{2} = \left( 2 \times 5\right)^{2} a true statement?

d

Calculate 4^{2} \times 2^{2} using the above method.

Square roots
4

Given that we know 5 \times 5 = 25. What is \sqrt{25}?

5

Evaluate the following:

a
\sqrt{4}
b
\sqrt{16}
c
\sqrt{121}
d
\sqrt{144} + \sqrt{64}
e
\sqrt{144} - \sqrt{64}
f
\sqrt{6^{2} + 8^{2}}
g
\sqrt{13^{2} - 12^{2}}
h
\sqrt{13^{2}} - \sqrt{12^{2}}
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