Question

simplify: $19sqrt{6} + 25sqrt{7} + 3sqrt{6} + 6sqrt{7}$
a. $22sqrt{6} - 31sqrt{7}$
b. $3sqrt{6} + 31sqrt{7}$
c. $22sqrt{6} + 31sqrt{7}$
d. $22sqrt{7} + 31sqrt{6}$
reset selection

Explanation:

Step1: Group like terms

We have terms with $\sqrt{6}$ and terms with $\sqrt{7}$. Group them together: $(19\sqrt{6} + 3\sqrt{6}) + (25\sqrt{7} + 6\sqrt{7})$

Step2: Combine like terms

For the $\sqrt{6}$ terms: $19\sqrt{6}+3\sqrt{6}=(19 + 3)\sqrt{6}=22\sqrt{6}$
For the $\sqrt{7}$ terms: $25\sqrt{7}+6\sqrt{7}=(25 + 6)\sqrt{7}=31\sqrt{7}$

Step3: Combine the results

Put the combined terms together: $22\sqrt{6}+31\sqrt{7}$

Answer:

C. $22\sqrt{6} + 31\sqrt{7}$