Question

18/√13+1
rationalize ​

Answer 1

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Answer 2

Hello friend :)

$\rm \red{Rationalisation \: the\: following } \: \dashrightarrow\tt\frac{18}{ \sqrt{13} + 1 }$

Rationalising factor ➝ √13 - 1 [Opposite sign of the given denominator]

$\dashrightarrow \tt \: \frac{18}{ \sqrt{13} + 1 } \times \frac{ \sqrt{13} - 1}{ \sqrt{13} - 1 } \\ \\ \tt\dashrightarrow \frac{18( \sqrt{13} - 1) }{ {( \sqrt{13} )}^{2} - {(1)}^{2} } \red{\: \: \: \:[ \sf\green{ {x}^{2} - {y}^{2} = (x + y)(x - y) }]} \\ \\ \tt \dashrightarrow \: \frac{18 \sqrt{13} - 18}{( \sqrt{13} \times \sqrt{13}) - (1 \times 1) } \\ \\ \tt\dashrightarrow \: \frac{18 \sqrt{13} - 18}{ \sqrt{169} - 1} \\ \\ \tt\dashrightarrow \: \frac{18 \sqrt{13} - 18 }{13 - 1} \\ \\ \tt \dashrightarrow \: \frac{18 \sqrt{13} - 18}{12} \\ \\ \tt \dashrightarrow \frac{ \cancel6(3\sqrt{13} - 3) }{ \cancel{12 \: }_2} \\ \\ \therefore \boxed {\red{\frac{3 \sqrt{13} - 3}{2} }} \: \: \: \: \blue{[Answer]}$

$\overbrace{ \underbrace{ \fcolorbox{white}{pink}{ \blue\dag \tt Additional Information\red\dag}}}$

• suppose we are given a number whose denominator is irrational. Then, the process of converting it into an equivalent expression whose denominator is a rational number by multiplying its numerator and denominator by a suitable number is called Rationalisation.

• If the product of two irrational number is rational then each one is called the rationalising factor of the other.

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