Question

If √6 + √2/√6 - √2 = a + √b, then find the values of a and b

Answer 1

TOPIC: TO RATIONALIZE THE DENOMINATOR

$\frac{\sqrt{6} + \sqrt{2}}{ \sqrt{6} - \sqrt{2} } \times \frac{ \sqrt{6} + \sqrt{2} }{\sqrt{6} + \sqrt{2}} \\ \\ = \frac{( \sqrt{6} + \sqrt{2})^{2} }{4} \\ \\ = \frac{6 + 2 + 4 \sqrt{3} }{4} \\ \\ = \frac{8 + 4 \sqrt{3} }{4} = \frac{4(2 + \sqrt{3} )}{4} \\ \\ = 2 + \sqrt{3}$

→ on comparing it with a + √b, we have,

★ a= 2 and b= √3


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