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Given that $\sqrt{3}$ is an irrational number, prove that $2-5\sqrt{3}$ is also an irrational number.
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Ans. Let $2 - 5\sqrt{3} = r$ be a rational number (1/2 Mark)
So, $\sqrt{3} = \frac{2-r}{5}$ (1 Mark)
RHS is a rational number
So LHS is a rational number which is a contradiction (1 Mark)
Hence, $2 - 5\sqrt{3}$ is an irrational number. (1/2 Mark)
So, $\sqrt{3} = \frac{2-r}{5}$ (1 Mark)
RHS is a rational number
So LHS is a rational number which is a contradiction (1 Mark)
Hence, $2 - 5\sqrt{3}$ is an irrational number. (1/2 Mark)