Question

If 7√3/√10+√3 = a+b√10 then find the value of a/b

Answer 1

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$-\sqrt{3}$

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LHS:

$\dfrac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} }$

Rationalising numerator and denominator,

$\dfrac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \dfrac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} } \\ \\ \dfrac{7 \sqrt{3} ( \sqrt{10} - \sqrt{3} ) }{ ({ \sqrt{10}) }^{2} - {( \sqrt{3} )}^{2} } \\ \\ \dfrac{7 \sqrt{30} - 21 }{10 - 3} \\ \\ \dfrac{7 \sqrt{30} - 7 \times 3}{7} \\ \\ \frac{\not{7}( \sqrt{3} \times \sqrt{10} - 3) }{\not{ 7}} \\ \\ \sqrt{3} \times \sqrt{10} - 3 \\ \\ - 3 + \sqrt{3} \times \sqrt{10} = a + b \times \sqrt{10}$

Comparing the values we get:

a = -3 and b = $\sqrt{3}$

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