Question

Simplify the expression. $$\sqrt{3}(5 \sqrt{2}+\sqrt{3})$$

Short answer

The simplified expression is \(5\sqrt{6} + 3\)

Step-by-step solution

Distribute \(\sqrt{3}\)

Start by distributing the \(\sqrt{3}\) to each term inside the parenthesis: \( \sqrt{3} \times 5\sqrt{2} + \sqrt{3} \times \sqrt{3}\)

Multiply the square roots

To multiply the square roots, multiply the numbers under the square roots: \(5\sqrt{6} + 3\)

Write the final simplified expression

The expression is simplified as \(5\sqrt{6} + 3\)