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Mathematics
Mathematics
Problem
Calculate the exact value of each of the following and then state whether your final answer is a rational number or an irrational number. Show all steps clearly. a. (i)
(
2
+
3
)
2
−
(
3
2
−
1
)
(\sqrt{2} + 3)^2 - (3\sqrt{2} - 1)
(
2
+
3
)
2
−
(
3
2
−
1
)
b. (ii)
7
2
÷
(
2
−
3
)
\dfrac{7}{2} \div \left(2 - \sqrt{3}\right)
2
7
÷
(
2
−
3
)
c. (iii)
(
5
−
2
3
)
(
5
+
2
3
)
\left(5 - 2\sqrt{3}\right)\left(5 + 2\sqrt{3}\right)
(
5
−
2
3
)
(
5
+
2
3
)
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