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