Problem 32 - Algebra and Trigonometry

Question

Perform the indicated operations and write the result in standard form. $$ 5 \sqrt{-8}+3 \sqrt{-18} $$

Step-by-Step Solution

Answer

The result in standard form is \(19i\sqrt{2}\).

Step 1: Break down the square roots

Firstly, break down the square roots by simplifying each under the square root sign. Write \(\sqrt{-8}\) as \(2i\sqrt{2}\) and \(\sqrt{-18}\) as \(3i\sqrt{2}\). The equation becomes: \[ 5 * 2i\sqrt{2} + 3 * 3i\sqrt{2} \]

Step 2: Simplify the equation

Perform multiplication in both terms. The equation becomes: \[ 10i\sqrt{2} + 9i\sqrt{2} \]

Step 3: Combine like terms

Add the two terms together as they both have \(i\sqrt{2}\) in common. Thus the equation simplifies to: \[ (10i + 9i)\sqrt{2} \]

Step 4: Get the final answer

Simplify the equation to get the standard form: \[ 19i\sqrt{2} \]