Question

rationalise the denominator 1÷√7-2

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Answer 1

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Answer 2

Rationalise the denominator



${ \huge{ \bold { \red{ \frac{1}{ \sqrt{7} - 2}}}} }$




${ \bold{ \huge{ \mathfrak{ \underline{ \underline{ \purple{ Solution:-}}}}}}}$



${ \bold{ \huge{ \frac{1}{ \sqrt{7} - 2}}}}$



▪ cross multiplying both the numerator and denominator by( root 7 +2)...



${ \bold{ \huge{ = \frac{1}{ \sqrt{7} - 2} \times \frac{ \sqrt{7} + 2}{ \sqrt{7} + 2}}}}$



${ \bold{ \huge{ = \frac{ \sqrt{7} + 2 }{( \sqrt{7 } - 2)( \sqrt{7} + 2)}}} }$



▪ using the algebraic identity in the denominator....



${ \bold{ \underline{ \purple{(a - b)(a + b) = {a}^{2} - {b}^{2} }}}}$



${ \bold{ \huge{ = \frac{ \sqrt{7} + 2 }{ {( \sqrt{7} )}^{2} - {2}^{2} }}}}$



${ \huge{ \bold{ = \frac{ \sqrt{7} + 2 }{7 - 4}}}}$



${ \bold{ \huge{ \red{ = \frac{ \sqrt{7} + 2 }{3}}}}}$