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This section comprises $6$ Short Answer (SA) type questions of $3$ marks each.
Given that $\sqrt{5}$ is an irrational number, prove that $3+2\sqrt{5}$ is also an irrational number.
Given that $\sqrt{5}$ is an irrational number, prove that $3+2\sqrt{5}$ is also an irrational number.
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Let $3 + 2\sqrt{5} = r$ be a rational number (1/2 Mark)
So $\sqrt{5} = \frac{r-3}{2}$ (1 Mark)
RHS is a rational number
So LHS is a rational number which is a contradiction (1 Mark)
Hence $3 + 2\sqrt{5}$ is an irrational number. (1/2 Mark)
So $\sqrt{5} = \frac{r-3}{2}$ (1 Mark)
RHS is a rational number
So LHS is a rational number which is a contradiction (1 Mark)
Hence $3 + 2\sqrt{5}$ is an irrational number. (1/2 Mark)