Question

Simplify √(√30+√21/√30-√21​)
With steps!

Answer 1

$Given \: \sqrt{\frac{ ( \sqrt{30} + \sqrt{21}) }{ ( \sqrt{30} - \sqrt{21})}} \\= \sqrt{\frac{ ( \sqrt{30} + \sqrt{21}) ( \sqrt{30} + \sqrt{21})}{ ( \sqrt{30} - \sqrt{21})( \sqrt{30} + \sqrt{21})}} \\= \sqrt{\frac{ ( \sqrt{30} + \sqrt{21})^{2}}{ ( \sqrt{30})^{2} - (\sqrt{21})^{2}}}\\= \sqrt{ \frac{(\sqrt{30} + \sqrt{21})^{2}}{30 - 21}} \\= \sqrt{ \frac{(\sqrt{30} + \sqrt{21})^{2}}{9}} \\= \sqrt{ \frac{(\sqrt{30} + \sqrt{21})^{2}}{3^{2}}} \\= \frac{(\sqrt{30} + \sqrt{21})}{3}}$

Therefore.,

$\red{ \sqrt{\frac{ ( \sqrt{30} + \sqrt{21}) }{ ( \sqrt{30} - \sqrt{21})}}}\\\green { = \frac{(\sqrt{30} + \sqrt{21})}{3}}$

••♪

Answer 2

Step-by-step explanation:

$\sf \bf We \: have,$

$\sf \sqrt{\dfrac{\sqrt{30}+\sqrt{21}}{\sqrt{30}-\sqrt{21}}}$

$\sf \implies \sqrt{\dfrac{\sqrt{30}+\sqrt{21}}{\sqrt{30}-\sqrt{21}}×\dfrac{\sqrt{30}+\sqrt{21}}{\sqrt{30}+\sqrt{21}} }$

$\sf \implies \sqrt{\dfrac{(\sqrt{30}+\sqrt{21})^2}{(\sqrt{30})^2-(\sqrt{21})^2} }$

$\sf \implies \sqrt{\dfrac{(\sqrt{30}+\sqrt{21})^2}{30-21} }$

$\sf \implies \sqrt{\dfrac{(\sqrt{30}+\sqrt{21})^2}{9} }$

$\sf \implies \sqrt{\dfrac{(\sqrt{30}+\sqrt{21})^2}{(3)^2} }$

$\sf \implies \underline{\boxed{\bf \dfrac{\sqrt{30}+\sqrt{21}}{3} }}$