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# If $$\Large \sqrt{2}$$ = 1.4142, then the value of $$\Large \frac{7}{4 + \sqrt{2}}$$ is

 A) 3.5858 B) 4.4142 C) 1.2929 D) 1.5858

 C) 1.2929

$$\Large \frac{7}{4+\sqrt{2}} = \frac{7}{4+\sqrt{2}} \times \frac{ \left(4 - \sqrt{2}\right) }{ \left(4 - \sqrt{2}\right) }$$

= $$\Large \frac{7 \left(4-\sqrt{2}\right) }{16 - 2}$$

$$\Large Because \left(a+b\right) \times \left(a-b\right) = a^{2} - b^{2}$$

= $$\Large \frac{7 \left(4-\sqrt{2}\right)}{14} = \frac{4-\sqrt{2}}{2} = \frac{4-1.4142}{2}$$

= $$\Large \frac{2.5858}{2} = 1.2929$$

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

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