Question

simplify.

(3sqrt{2} + 5sqrt{7} - 5sqrt{2} + 3sqrt{7})

select one:
a. (8sqrt{2} + 8sqrt{7})
b. (-2sqrt{2} + 8sqrt{7})
c. (6sqrt{9})
d. (52)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Group like terms

Group the terms with \(\sqrt{2}\) together and the terms with \(\sqrt{7}\) together:

$$ (3\sqrt{2} - 5\sqrt{2}) + (5\sqrt{7} + 3\sqrt{7}) $$

Step 2: Combine coefficients

Combine the coefficients for each set of like radicals:

$$ (3 - 5)\sqrt{2} + (5 + 3)\sqrt{7} $$

$$ -2\sqrt{2} + 8\sqrt{7} $$

Answer:

b. \(-2\sqrt{2} + 8\sqrt{7}\)