Question

simplify 1/√2+1+1/√3+√2+1/√4+√3​

Answer 1

Answer:

=$\sqrt{4}-1$ ans

Step-by-step explanation:

the question is $\frac{1}{\sqrt{2}+1 } +\frac{1}{\sqrt{3}+\sqrt{2} } +\frac{1}{\sqrt{4}+\sqrt{3} }$

first step :- change sign of denominator after that multiply and divide

so it will be $\frac{1}{\sqrt{2}+1 } . \frac{\sqrt{2}-1}{\sqrt{2}-1 } +\frac{1}{\sqrt{3}+\sqrt{2} }. \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2} } +\frac{1}{\sqrt{4}+\sqrt{3} }.\frac{\sqrt{4}-\sqrt{3} }{\sqrt{4}-\sqrt{3} }$

we use formula $(a+b)(a-b) = a^{2}-b^{2}$

so it will be $\frac{\sqrt{2}-1}{(\sqrt{2})^{2} -1 } +\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3})^{2} -(\sqrt{2})^{2} } +\frac{\sqrt{4}-\sqrt{3} }{(\sqrt{4})^{2} -(\sqrt{3})^{2} }$

now simplify above equation

=$\frac{\sqrt{2}-1}{2 -1 } +\frac{\sqrt{3}-\sqrt{2}}{{3-2} } +\frac{\sqrt{4}-\sqrt{3} }{4-3}$

=$\sqrt{2}-1} +\sqrt{3}-\sqrt{2}} +\sqrt{4}-\sqrt{3} }$

=$-1} +\sqrt{4}$

=$\sqrt{4}-1$ ans

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have a great day (: