\sqrt{15+2\sqrt{15}+2\sqrt{21}+2\sqrt{35}+\sqrt{15-2\sqrt{15}-2\sqrt{21}+2\sqrt{35}=

AP ICET 2015 Paper

Question : 81 of 200

Marks: +1, -0

√{15+2√{15}+2√{21}+2√{35}}+√{15-2√{15}-2√{21}+2√{35}}=

Solution:

Given expression :`

√{15+2√{15}+2√{21}+2√{35}}+√{15-2√{15}-2√{21}+2√{35}}=

=√{(√{3})^{2}+(√{5})^{2}+(√{7})^{2}+2(√{3})(√{5})+2(√{3})(√{7})+2(√{5})(√{7})}+

=√{(√{3}+√{5}+√{7})^{2}}+√{(√{5}+√{7}-√{3})^{2}}=

√{3}+√{5}+√{7}+√{5}+√{7}-√{3}=2(√{5}+√{7})

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