Question

The rationalising factor of 4 + root 5

Answer 1

$\textbf{Given:}$

$\mathsf{4+\sqrt{5}}$

$\textbf{To find:}$

$\textsf{Rationalising factor of}\;\mathsf{4+\sqrt{5}}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{(4+\sqrt{5})(4-\sqrt{5})}$

$\textsf{Using the identity}$

$\boxed{\mathsf{(a+b)(a-b)=a^2-b^2}}$

$\mathsf{=4^2-\sqrt{5}^2}$

$\mathsf{=16-5}$

$\mathsf{=11,\;a\;rational\;number}$

$\therefore\mathsf{Rationalising\;factor\;of\;4+\sqrt{5}\;is\;4-\sqrt{5}}$

$\textbf{Find more:}$

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