Question : If $\sqrt5=2.236$, then what is the value of $\frac{\sqrt5}{2}+\frac{5}{3\sqrt5}-\sqrt{45}$?
Option 1: – 8.571
Option 2: – 4.845
Option 3: – 2.987
Option 4: – 6.261
Correct Answer: – 4.845
Solution : Given: $\sqrt{5} = 2.236$ $\frac{\sqrt{5}}{2} + \frac{5}{3\sqrt{5}} - \sqrt{45}$ Now evaluate the equation, = $ \frac{\sqrt{5}\times3\sqrt{5} + 5\times2-3\sqrt{5}\times2\times3\sqrt{5}}{2\times3\sqrt{5}}$ = $ \frac{15 + 10 - 90}{2\times3\sqrt{5}}$ = $ -\frac{65}{2\times3\sqrt{5}}$ Rationalising the fraction = $ -\frac{65\sqrt{5}}{30}$ Put the value of $\sqrt{5} = 2.236$ = $-\frac{65\times 2.236}{30} = -4.845$ Hence, the correct answer is – 4.845.
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