Answer:
[tex]\sqrt{2}-\sqrt{5}+\sqrt{10}[/tex]
Step-by-step explanation:
we have
[tex]\sqrt{2}-\frac{\sqrt{10}}{\sqrt{2}} +\sqrt{10}[/tex]
we know that
[tex]\sqrt{10}=\sqrt{2}*\sqrt{5}[/tex]
substitute
[tex]\sqrt{2}-\frac{\sqrt{2}*\sqrt{5}}{\sqrt{2}} +\sqrt{10}[/tex]
simplify
[tex]\sqrt{2}-\sqrt{5}+\sqrt{10}[/tex]
Answer:
[tex]\frac{1}{2}(\sqrt{5}-3)[/tex]
Step-by-step explanation:
Given expression,
[tex]\frac{\sqrt{2}-\sqrt{10}}{\sqrt{2}+\sqrt{10}}[/tex]
By rationalising the denominator,
[tex]=\frac{\sqrt{2}-\sqrt{10}}{\sqrt{2}+\sqrt{10}}\times\frac{\sqrt{2}-\sqrt{10}}{\sqrt{2}-\sqrt{10}}[/tex]
[tex]=\frac{(\sqrt{2}-\sqrt{10})^2}{(\sqrt{2})^2-(\sqrt{10})^2}[/tex]
( ∵ ( a + b ) ( a - b ) = a² - b² )
[tex]=\frac{(\sqrt{2}-\sqrt{10})^2}{2-10}[/tex]
[tex]=\frac{2+10-2\sqrt{20}}{-8}[/tex]
( ∵ (a + b)² = a² + 2ab + b² )
[tex]=-\frac{1}{8}(12-4\sqrt{5})[/tex]
[tex]=-\frac{1}{2}(3-\sqrt{5})[/tex]
[tex]=\frac{1}{2}(\sqrt{5}-3)[/tex]
