Example Question 1

Example corresponding to question 1 in algebra_1.

Example 1


$\sqrt[3]{54}+\sqrt[3]{16}=$

  1. $\sqrt[3] {70}$

  2. $5 \sqrt[3] 2$

  3. $\dfrac{70}{3}$

  4. $3\sqrt[3] 6 + 4$

  5. $\dfrac{35}{3}$

Solution


  1. If we examine the 5 possible answers, we come up to the conclusion that we need to simplify the given expression. In order to simplify expressions with radicands, we need to rewrite them so that they have the same radicand. So we first rewrite the two radicands in the given expression as follows:

    $\sqrt[3]{54}=\sqrt[3]{2 \cdot 27} = \sqrt[3] 2 \sqrt[3]{3^3}=3\sqrt[3] 2$

    $\sqrt[3]{16}=\sqrt[3]{2 \cdot 8} = \sqrt[3] 2 \sqrt[3]{2^3}=2\sqrt[3] 2$

  2. Substitute in the given expression and simplify

    $\sqrt[3]{54}+\sqrt[3]{16}= 3\sqrt[3] 2 + 2\sqrt[3] 2 = 5 \sqrt[3] 2$

    Answer B