Question

simplify the given expression.

\\((4\sqrt{2} + 8) + (5\sqrt{2} - 15)\\)

\\((4\sqrt{2} + 8) + (5\sqrt{2} - 15) = \\)

(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Identify the terms

We begin with the given expression:

$$ (4\sqrt{2} + 8) + (5\sqrt{2} - 15) $$

Using the Algebraic Expressions knowledge point, we can remove the parentheses because the operation between the groups is addition.

$$ 4\sqrt{2} + 8 + 5\sqrt{2} - 15 $$

Group like terms

Next, we group the radical terms together and the constant integer terms together.

$$ (4\sqrt{2} + 5\sqrt{2}) + (8 - 15) $$

Combine the radical terms

We combine the coefficients of the like radical terms containing \(\sqrt{2}\).

$$ (4 + 5)\sqrt{2} = 9\sqrt{2} $$

Combine the constant terms

We calculate the sum of the constant integers.

$$ 8 - 15 = -7 $$

Write the final simplified expression

Combining the simplified parts gives the final exact expression.

$$ 9\sqrt{2} - 7 $$

Answer:

\((4\sqrt{2} + 8) + (5\sqrt{2} - 15) =\) <blank>\(9\sqrt{2} - 7\)</blank>