Question

What is the exact value of the expression sqrt(32) + sqrt(75) - sqrt(98)? Simplify Completely.

Answer 1

The approach is to find squares in each of the components. As an example 32 = 16x2, where 16 is a square of 4. Therefore,
\[\sqrt{32}=\sqrt{16\times2}=\sqrt{16}\sqrt{2}=4\sqrt{2}\]

A similar approach should be taken for each of the other numbers. 75 = 25x3 and 98 = 49x2. Using the method above,
\[\sqrt{75}=\sqrt{25*3}=\sqrt{25}\sqrt{3}=5\sqrt{3}\]
\[\sqrt{98}=\sqrt{49*2}=\sqrt{49}\sqrt{2}=7\sqrt{2}\]

Putting it all together now:
\[\sqrt{32}+\sqrt{75}-\sqrt{98}=4\sqrt{2}+5\sqrt{3}-7\sqrt{2}\]

combining common terms for final answer:
\[\sqrt{32}+\sqrt{75}-\sqrt{98}=5\sqrt{3}-3\sqrt{2}\]