How would you simplify and do these problems?
(square root of) 2/5 + (square root of) 1/2
8 - (square root of) 5/7
I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
How would you simplify and do these problems?
(square root of) 2/5 + (square root of) 1/2
8 - (square root of) 5/7
I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
$\displaystyle \displaystyle \sqrt{\frac{2}{5}} + \sqrt{\frac{1}{2}} = \sqrt{\frac{4}{10}} + \sqrt{\frac{5}{10}}$
$\displaystyle \displaystyle = \frac{\sqrt{4}}{\sqrt{10}} + \frac{\sqrt{5}}{\sqrt{10}}$
$\displaystyle \displaystyle = \frac{\sqrt{4} + \sqrt{5}}{\sqrt{10}}$
$\displaystyle \displaystyle = \frac{2 + \sqrt{5}}{\sqrt{10}}$
$\displaystyle \displaystyle = \frac{\sqrt{10}(2 + \sqrt{5})}{10}$
$\displaystyle \displaystyle = \frac{2\sqrt{10} + \sqrt{50}}{10}$
$\displaystyle \displaystyle = \frac{2\sqrt{10} + \sqrt{25}\sqrt{2}}{10}$
$\displaystyle \displaystyle = \frac{2\sqrt{10} + 5\sqrt{2}}{10}$.