Question

how to solve double square root surds √27-10√2?

Answer 1

$\sqrt{27 - 10 \sqrt{2} }$

=

$\sqrt{25 + 2 - 2 \times 5 \times \sqrt{2} }$

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

$= \sqrt{ {(5 + \sqrt{2)} }^{2} }$

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