Question

simplify: $16sqrt{2} + 24sqrt{3} + 14sqrt{2} + 4sqrt{3}$
a. $14sqrt{2} + 28sqrt{3}$
b. $30sqrt{2} + 28sqrt{3}$
c. $30sqrt{3} + 28sqrt{2}$
d. $30sqrt{2} - 28sqrt{3}$
reset selection

Explanation:

Step1: Group like terms

Group the terms with $\sqrt{2}$ and the terms with $\sqrt{3}$:
$(16\sqrt{2} + 14\sqrt{2}) + (24\sqrt{3} + 4\sqrt{3})$

Step2: Combine like terms

For the $\sqrt{2}$ terms: $16\sqrt{2}+14\sqrt{2}=(16 + 14)\sqrt{2}=30\sqrt{2}$
For the $\sqrt{3}$ terms: $24\sqrt{3}+4\sqrt{3}=(24 + 4)\sqrt{3}=28\sqrt{3}$

Step3: Combine results

Put the combined terms together: $30\sqrt{2}+28\sqrt{3}$

Answer:

B. $30\sqrt{2} + 28\sqrt{3}$