Question

determine the conjugate radical of the expression

\\-\sqrt{8} + 3\sqrt{5}\\

• \\(-\sqrt{8} - 3\sqrt{5}\\)
• \\(-\sqrt{8} + 3\sqrt{5}\\)
• \\(\sqrt{8} + 3\sqrt{5}\\)
• \\(-\sqrt{8} + 5\sqrt{3}\\)

Explanation:

Identify the given expression

The given radical expression is:

$$-\sqrt{8} + 3\sqrt{5}$$

Define conjugate radicals

For any binomial radical expression of the form \(a\sqrt{x} + b\sqrt{y}\), its conjugate radical is obtained by changing the sign of the second term:

$$a\sqrt{x} - b\sqrt{y}$$

Apply the definition

We change the sign of the second term \(3\sqrt{5}\) to \(-3\sqrt{5}\):

$$-\sqrt{8} - 3\sqrt{5}$$

Match with options

Comparing our result with the given choices:

• Option 1: \(-\sqrt{8} - 3\sqrt{5}\)
• Option 2: \(-\sqrt{8} + 3\sqrt{5}\)
• Option 3: \(\sqrt{8} + 3\sqrt{5}\)
• Option 4: \(-\sqrt{8} + 5\sqrt{3}\)

The first option matches our result.

Answer:

• (A) \(-\sqrt{8} - 3\sqrt{5}\) (Correct answer)
• (B) \(-\sqrt{8} + 3\sqrt{5}\)
• (C) \(\sqrt{8} + 3\sqrt{5}\)
• (D) \(-\sqrt{8} + 5\sqrt{3}\)