Question

indices : (√32 - √5 )½ ( √32 + √5 )½​

Answer 1

$Given \: ( \sqrt {32} - \sqrt{5} )^{\frac{1}{2}} ( \sqrt {32} + \sqrt{5} )^{\frac{1}{2}}$

$= [( \sqrt {32} - \sqrt{5} )( \sqrt {32} + \sqrt{5} )]^{\frac{1}{2}}$

$\boxed { \pink { \sqrt{a} \times \sqrt{b} = \sqrt{a \times b } }}$

$= \sqrt{ (\sqrt{32})^{2} - (\sqrt{5})^{2}}$

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

$= \sqrt { 32 - 5 } \\= \sqrt{27} \\= \sqrt{3 \times 3 \times 3 } \\= 3\sqrt{3}$

Therefore.,

$\red{ ( \sqrt {32} - \sqrt{5} )^{\frac{1}{2}} ( \sqrt {32} + \sqrt{5} )^{\frac{1}{2}}} \green { = 3\sqrt{3} }$

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