Simplify \(\sqrt{50} + \frac{10}{\sqrt{2}}\)
A
10
B
10\(\sqrt{2}\)
C
20
D
20\(\sqrt{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\sqrt{50} + \frac{10}}{\sqrt{2}} = \(\frac{\sqrt{50}}{1} + \sqrt{10}{\sqrt{2}}\)
= \(\frac{\sqrt{50 \times 2} + 10}{\sqrt{2}}\)
= \(\frac{\sqrt{100} + 10}{\sqrt{2}}\)
= \(\frac{10 + 10}{\sqrt{2} = \frac{20}{\sqrt{2}}\)
= \(\frac{20}{\sqrt{2}}\) \times \frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{20\sqrt{2}}{2}\)
= 10\(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36326)