A) 1.00
B) 1.25
C) 1.50
D) 2.25
Correct Answer: A
Solution :
(a): \[\frac{1}{\sqrt{3.25}+\sqrt{2.25}}\] =\[\frac{1}{\left( \sqrt{3.25}+\sqrt{2.25} \right)}\times \frac{\sqrt{3.25}-\sqrt{2.25}}{\sqrt{3.25}-\sqrt{2.25}}\] =\[\frac{\sqrt{3.25}-\sqrt{2.25}}{3.25-2.25}=\sqrt{3.25}-\sqrt{2.25}\] Similarly, \[\frac{1}{\sqrt{4.25}+\sqrt{3.25}}=\sqrt{4.25}-\sqrt{3.25}\] \[\frac{1}{\sqrt{5.25}+\sqrt{4.25}}=\sqrt{5.25}-\sqrt{4.25}\] \[\frac{1}{\sqrt{6.25}+\sqrt{5.25}}=\sqrt{6.25}-\sqrt{5.25}\] \[\therefore \]Expression \[=\sqrt{3.25}-\sqrt{2.25}+\sqrt{4.25}-\sqrt{3.25}+\sqrt{5.25}-\sqrt{4.25}+\sqrt{6.25}-\sqrt{5.25}\]\[=\sqrt{6.25}-\sqrt{2.25}=2.5-1.5=1\]
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