Question

If a= 7-4√3, find the value of √ +

1/√a.

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Answer 1

Answer:

Step-by-step explanation:

$a = 7-4\sqrt{3} \\\sqrt{a} = \sqrt{ 7-4\sqrt{3} } \\\sqrt{a}+\frac{1}{\sqrt{a} }= \sqrt{7-4\sqrt{3} } +\sqrt{\frac{1}{7-4\sqrt{3} } }\\=\frac{7-4\sqrt{3}+1 }{7-4\sqrt{3} } \\=\frac{7-4\sqrt{3}+1 }{7-4\sqrt{3} } *\frac{7+4\sqrt{3} }{7+4\sqrt{3} } \\ =\frac{(7-4\sqrt{3} )(7+4\sqrt{3})+(7+4\sqrt{3}) }{7^2-(4\sqrt{3})^2 } \\ =\frac{7^2-(4\sqrt{3})^2+(7+4\sqrt{3}) }{49-48 } \\ =1 + 7 + 4\sqrt{3} \\ =8 + 4\sqrt{3}\\\sqrt{a}+\frac{1}{\sqrt{a} } =4(2+\sqrt{3} )$