Question

(25+10√6)^1/2+(25-10√6)^1/2
Find the value of this....
Please answer quickly

Answer 1

Here

$\sqrt{25+10\sqrt{6}}$

=$25+2(5)\sqrt{6}$

=$25+2\sqrt{150}$

=$25+2\sqrt{(15)(10)}$

=$25+2\sqrt{15} \sqrt{10}$

=$15+10+2\sqrt{15} \sqrt{10}$

=$(\sqrt{15})^2+2\sqrt{15}\sqrt{10} +(\sqrt{10} )^2$

=$(\sqrt{15}+\sqrt{10})^2$

Hence

$\sqrt{25+10\sqrt{6}} =\sqrt{(\sqrt{15}+\sqrt{10})^2} =\sqrt{15} +\sqrt{10}$

Similarly

$\sqrt{25-10\sqrt{6}} =\sqrt{(\sqrt{15}-\sqrt{10})^2} =\sqrt{15} -\sqrt{10}$

Adding we get

$\sqrt{25+10\sqrt{6}} +\sqrt{25-10\sqrt{6}} =\sqrt{15}+\sqrt{10}+\sqrt{15}-\sqrt{10} =2\sqrt{15}$

Hence

$\sqrt{25+10\sqrt{6}} +\sqrt{25-10\sqrt{6}}=2\sqrt{15}$

Answer 2

Step-by-step explanation:

the correct answer is 2√15