Question

Express 7+√5÷3√5 in the form a+b√5

Answer 1

Answer:

$\frac{7\sqrt{5}}{15}+\frac{1}{3}$

Step-by-step explanation:

Rationalising the denominator we get,

$\frac{7+\sqrt{5}}{3\sqrt{5}} = \frac{7+\sqrt{5}}{3\sqrt{5}}(\frac{3\sqrt{5}}{3\sqrt{5}})$

$=\frac{21\sqrt{5}}{45} +\frac{15}{45}\\ =\frac{7\sqrt{5}}{15}+\frac{1}{3}\\where \\a=\frac{1}{3}\\b=\frac{7}{15}$

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