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The greatest among the numbers $${\left( {2.89} \right)^{0.5}},$$   $$2 - {\left( {0.5} \right)^2},$$   $$1 + \frac{{0.5}}{{1 - \frac{1}{2}}},$$   $$\sqrt 3 $$  is = ?

The greatest among the numbers $${\left( {2.89} \right)^{0.5}},$$   $$2 - {\left( {0.5} \right)^2},$$   $$1 + \frac{{0.5}}{{1 - \frac{1}{2}}},$$   $$\sqrt 3 $$  is = ? Correct Answer $$1 + \frac{{0.5}}{{1 - \frac{1}{2}}}$$

$$\eqalign{ & {\left( {2.89} \right)^{0.5}} = {\left( {2.89} \right)^{\frac{5}{{10}}}} \to \sqrt {2.89} \to 1.7 \cr & {\text{2}} - {\left( {0.5} \right)^2} = 2 - 0.25 \to 1.75 \cr & 1 + \frac{{0.5}}{{1 - \frac{1}{2}}} = 1 + \frac{{0.5}}{{0.5}} \to 1 + 1 \to 2 \leftarrow {\text{Greatest}} \cr & \sqrt 3 = 1.732 \cr} $$

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