Simplify Square Root

This example is about simplifying expressions with square root .

Example 1


The expression $\dfrac{7\sqrt2 + \sqrt{50}}{3\sqrt2}$ simplifies to

  1. $3$
  2. $0$
  3. $8\sqrt2$
  4. $4$
  5. $8$

Solution

This example is about simplifying expressions with square roots.

  1. 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 $\sqrt 2$

    $\sqrt{50}=\sqrt{2\cdot 25}=\sqrt2\cdot \sqrt{25}=5\sqrt 2$


  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