Substitution and Evaluation - Tutorial

Examples corresponding to problems in algebra_1.

Example 1


$\dfrac{7\sqrt2 + \sqrt{50}}{3\sqrt2}=$

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

Solution


  1. If we examine the 5 possible answers, we come up to the conclusion that we need to simplify the given expression. The only 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}} $

    $=\dfrac{12}{4}$

    $= 4$