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Example 1
The expression $\dfrac{7\sqrt2 + \sqrt{50}}{3\sqrt2}$ simplifies to
- $3$
- $0$
- $8\sqrt2$
- $4$
- $8$
Solution
This example is about simplifying expressions with square roots.
- If we examine the 5 possible answers, we come up to the conclusion that we need to simplify the given expression. One way to simplify the given expression is to change $\sqrt{50}$ into an expression containing $\sqrt 2$
$\sqrt{50}=\sqrt{2\cdot 25}=\sqrt2\cdot \sqrt{25}=5\sqrt 2$
- Substitute in the given expression and simplify
$\dfrac{7\sqrt2 + \sqrt{50}}{3\sqrt2}$
$= \dfrac{7\sqrt2 + 5\sqrt{2}}{3\sqrt2}$
Group terms in numerator
$=\dfrac{12\sqrt2}{3\sqrt2}$
Cancel $\sqrt2$ as follows
$=\dfrac{12\colorcancel{red}{\sqrt 2}}{3\colorcancel{red}{\sqrt 2}}$
$=\dfrac{12}{4}$
$= 4$
Answer D
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