Question

RATIONALIZE OF DENOMINATOR:

$\frac{1}{ \sqrt{8 } } \\ \\ \\ \\ \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$
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Answer 1

Answer:

1)

$\frac{ \sqrt{8} }{8}$

2)

$5 - 2 \sqrt{6}$

Step-by-step explanation:

Rationalizing is so easy , just multiple the denominator by the conjugate surds or Rationalizing factor .

Solution

$\frac{1}{ \sqrt{8} } \\ \\ \frac{1}{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } \\ \\ \frac{ \sqrt{8} }{ \sqrt{8}. \sqrt{8} } \\ \\ \frac{ \sqrt{8} }{8}$

ii)

$\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ \frac{( \sqrt{3} - \sqrt{2} )( \sqrt{3} - \sqrt{2}) }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} )} \\ \\ \frac{ {( \sqrt{3} - \sqrt{2} )}^{2} }{ {( \sqrt{3} )}^{2} - { (\sqrt{2} )}^{2} } \\ \\ \frac{ ({ \sqrt{3} )}^{2} + { (\sqrt{2} )}^{2} - 2. \sqrt{2}. \sqrt{3} }{3 - 2} \\ \\ \frac{3 + 2 - 2 \sqrt{6} }{1} \\ \\ 5 - 2 \sqrt{6}$

Answer 2

Answer:

$\huge\fcolorbox{black}{pink}{Answer-}$

Q.1)

$= > \frac{1}{ \sqrt{8} } \\ = > \frac{1 \times \sqrt{8} }{ \sqrt{8 } \times \sqrt{8} } \\ = > \frac{ \sqrt{8} }{8} \\ = > \frac{2 \sqrt{2} }{8} \\ = > \frac{ \sqrt{2} }{4}$

Q.2)

root3 - root2 / root3 + root2

= (root3-root2)(root3-root2)/(root3+root)(root3-root2)

= (root3-root2)^2/3-2

=3- 2root6 +2/ 1