The value of frac{15}{sqrt{10} + sqrt{20} + s | vedclass

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(C) Given expression: $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$Simplify the surds:$\sqrt{20} = 2\sqrt{5}$$\sqrt{40} = 2\sq

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$\sqrt{5}(1 + \sqrt{2})$

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(C) Given expression: $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$Simplify the surds:$\sqrt{20} = 2\sqrt{5}$$\sqrt{40} = 2\sqrt{10}$$\sqrt{80} = 4\sqrt{5}$Substitute these values into the denominator:Denominator $= \sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}$$= (1 + 2)\sqrt{10} + (2 - 1 - 4)\sqrt{5}$$= 3\sqrt{10} - 3\sqrt{5}$Now,the fraction becomes:$= \frac{15}{3(\sqrt{10} - \sqrt{5})} = \frac{5}{\sqrt{10} - \sqrt{5}}$Rationalize the denominator:$= \frac{5}{\sqrt{10} - \sqrt{5}} 	imes \frac{\sqrt{10} + \sqrt{5}}{\sqrt{10} + \sqrt{5}}$$= \frac{5(\sqrt{10} + \sqrt{5})}{10 - 5}$$= \frac{5(\sqrt{10} + \sqrt{5})}{5}$$= \sqrt{10} + \sqrt{5}$$= \sqrt{5}(\sqrt{2} + 1)$

The value of $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$ is

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