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-7/ROOT11 -ROOT 5 HOW TO SOLVE THIS QUE RATIONALISATION

Answer» <html><body><p><strong>Step-by-step explanation:</strong></p><p></p><p>Here, we have to <a href="https://interviewquestions.tuteehub.com/tag/rationalise-2244913" style="font-weight:bold;" target="_blank" title="Click to know more about RATIONALISE">RATIONALISE</a> the denominator of,</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20%5Cdfrac%7B-7%7D%7B%5Csqrt%7B11%7D%20-%20%5Csqrt%7B5%7D%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\"/></p><p></p><p>In order to rationalise the denominator of any fraction, we multiply the rationalising factor of the denominator with both the numerator and the denominator of the fraction.</p><p>Rationalising factor is <a href="https://interviewquestions.tuteehub.com/tag/also-373387" style="font-weight:bold;" target="_blank" title="Click to know more about ALSO">ALSO</a> the conjugate of the denominator. Rationalising factor of <strong>(</strong><strong>a</strong><strong> </strong><strong>-</strong><strong> </strong><strong>b</strong><strong>)</strong> is <strong>(</strong><strong>a</strong><strong> </strong><strong>+</strong><strong> </strong><strong>b</strong><strong>)</strong>. So, the rationalising factor of <strong>(</strong><strong>√</strong><strong>1</strong><strong>1</strong><strong> </strong><strong>-</strong><strong> </strong><strong>5</strong><strong>)</strong> is <strong>(</strong><strong>√</strong><strong>1</strong><strong>1</strong><strong> </strong><strong>+</strong><strong> </strong><strong>5</strong><strong>)</strong>.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20%5Cdfrac%7B-7%7D%7B%5Csqrt%7B11%7D%20-%20%5Csqrt%7B5%7D%7D%20%5Ctimes%20%5Cdfrac%7B%28%5Csqrt%7B11%7D%20%2B%20%5Csqrt%7B5%7D%29%7D%7B%28%5Csqrt%7B11%7D%20%2B%20%5Csqrt%7B5%7D%29%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\"/></p><p></p><p>Multiplying (√11 + √5) with both the numerator of the fraction.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20%5Cdfrac%7B-7%28%5Csqrt%7B11%7D%20%2B%20%5Csqrt%7B5%7D%29%20%7D%7B%28%5Csqrt%7B11%7D%20-%20%5Csqrt%7B5%7D%29%28%5Csqrt%7B11%7D%20%2B%20%5Csqrt%7B5%7D%29%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\"/></p><p></p><p>Performing multiplication in the numerator and by <a href="https://interviewquestions.tuteehub.com/tag/using-7379753" style="font-weight:bold;" target="_blank" title="Click to know more about USING">USING</a> identity <strong>(</strong><strong>a </strong><strong>+</strong><strong> </strong><strong>b)</strong><strong>(</strong><strong>a </strong><strong>-</strong><strong> </strong><strong>b)</strong><strong> </strong><strong>=</strong><strong> </strong><strong>a</strong><strong>²</strong><strong> </strong><strong>-</strong><strong> </strong><strong>b²</strong>, solving further in the denominator.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20%5Cdfrac%7B-7%5Csqrt%7B11%7D%20-7%5Csqrt%7B5%7D%7D%7B%28%5Csqrt%7B11%7D%29%5E2%20-%20%28%5Csqrt%7B5%7D%29%5E2%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\"/></p><p></p><p>Writing the squares of the <a href="https://interviewquestions.tuteehub.com/tag/numbers-22758" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBERS">NUMBERS</a> in the denominator.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20%5Cdfrac%7B-7%5Csqrt%7B11%7D%20-7%5Csqrt%7B5%7D%7D%7B11%20-5%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\"/></p><p></p><p>Performing subtraction in the denominator.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Cquad%20%5Cunderline%7B%20%5Cboxed%7B%20%5Cdfrac%7B%20%5Ctextbf%7B%20%5Ctextsf%7B-7%20%7D%7D%5Csqrt%7B%20%5Ctextbf%7B%20%5Ctextsf%7B11%20%7D%7D%7D%20-%20%5Ctextbf%7B%20%5Ctextsf%7B7%7D%7D%5Csqrt%7B%20%5Ctextbf%7B%20%5Ctextsf%7B5%20%7D%7D%7D%7D%7B%20%5Ctextbf%7B%20%5Ctextsf%7B%206%7D%7D%7D%7D%20%7D%20%5C%5C%20" title="\longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\"/></p><p></p><p><strong><u>Hence</u></strong><strong><u>,</u></strong><strong><u> </u></strong><strong><u>rationalised</u></strong><strong><u>!</u></strong></p><p></p><p></p></body></html>


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