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 in the denominator:$\sqrt{20} = 2\sqrt{

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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 in the denominator:$\sqrt{20} = 2\sqrt{5}$,$\sqrt{40} = 2\sqrt{10}$,$\sqrt{80} = 4\sqrt{5}$Substitute these values:$= \frac{15}{\sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}}$Combine like terms:$= \frac{15}{3\sqrt{10} - 3\sqrt{5}} = \frac{15}{3(\sqrt{10} - \sqrt{5})} = \frac{5}{\sqrt{10} - \sqrt{5}}$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}$Factor out $\sqrt{5}$:$= \sqrt{5}(\sqrt{2} + 1)$

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

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