/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 Perform the indicated operation(... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 50

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

Short Answer

Expert verified
The result of performing the indicated operation is \( 19i \sqrt{2} \).

Step by step solution

01

Rewrite square roots of negative numbers

Rewrite \( \sqrt{-8} \) and \( \sqrt{-18} \) as \( i \sqrt{8} \) and \( i \sqrt{18} \) respectively, to get the expression \( 5i \sqrt{8} + 3i \sqrt{18} \).
02

Simplify the square roots

Simplify \( \sqrt{8} \) and \( \sqrt{18} \) as \( \sqrt{4} \cdot \sqrt{2} \) and \( \sqrt{9} \cdot \sqrt{2} \) respectively, which further simplifies to \( 2 \sqrt{2} \) and \( 3 \sqrt{2} \). Substitute this to the expression from step 1, to get \( 5i \cdot 2 \sqrt{2} + 3i \cdot 3 \sqrt{2} \).
03

Simplify the multiplication

Perform the multiplication in the expression from step 2 to eventually get \( 10i \sqrt{2} + 9i \sqrt{2} \).
04

Combine like terms

Combine \( 10i \sqrt{2} \) and \( 9i \sqrt{2} \) to get the final result \( 19i \sqrt{2} \).

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