Question

simplify: $19sqrt{7} - 22sqrt{3} + 5sqrt{7} + 6sqrt{3}$
a. $24sqrt{7} + 16sqrt{3}$
b. $24sqrt{7} - 16sqrt{3}$
c. $5sqrt{7} - 16sqrt{3}$
d. $24sqrt{3} - 16sqrt{7}$
reset selection

Explanation:

Step1: Group like terms

Group the terms with \(\sqrt{7}\) and the terms with \(\sqrt{3}\) together: \((19\sqrt{7} + 5\sqrt{7}) + (-22\sqrt{3} + 6\sqrt{3})\)

Step2: Combine like terms

For the \(\sqrt{7}\) terms: \(19\sqrt{7}+5\sqrt{7}=(19 + 5)\sqrt{7}=24\sqrt{7}\)
For the \(\sqrt{3}\) terms: \(-22\sqrt{3}+6\sqrt{3}=(-22 + 6)\sqrt{3}=-16\sqrt{3}\)

Step3: Combine the results

Put the combined terms together: \(24\sqrt{7}-16\sqrt{3}\)

Answer:

B. \(24\sqrt{7}-16\sqrt{3}\)