Discover new knowledge and insights with IDNLearn.com's extensive Q&A platform. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

What is the simplified form of the following expression?

[tex]\[ 5 \sqrt{8} - \sqrt{18} - 2 \sqrt{2} \][/tex]

A. [tex]\( 2 \sqrt{2} \)[/tex]
B. [tex]\( 5 \sqrt{2} \)[/tex]
C. [tex]\( 9 \sqrt{2} \)[/tex]
D. [tex]\( 15 \sqrt{2} \)[/tex]


Sagot :

To simplify the expression [tex]\(5 \sqrt{8} - \sqrt{18} - 2 \sqrt{2}\)[/tex], let's first break down each term individually and then combine them step-by-step.

1. Simplify [tex]\(5 \sqrt{8}\)[/tex]:
[tex]\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2} \][/tex]
So:
[tex]\[ 5 \sqrt{8} = 5 \cdot 2 \sqrt{2} = 10 \sqrt{2} \][/tex]

2. Simplify [tex]\(\sqrt{18}\)[/tex]:
[tex]\[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2} \][/tex]

3. Consider [tex]\(2 \sqrt{2}\)[/tex], which is already in simplified form.

Now, combining all simplified terms:
[tex]\[ 5 \sqrt{8} - \sqrt{18} - 2 \sqrt{2} = 10 \sqrt{2} - 3 \sqrt{2} - 2 \sqrt{2} \][/tex]

Add up the coefficients of [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ (10 - 3 - 2) \sqrt{2} = 5 \sqrt{2} \][/tex]

Thus, the simplified form of the given expression is:
[tex]\[ 5 \sqrt{2} \][/tex]

So the correct simplified form is:
[tex]\[ \boxed{5 \sqrt{2}} \][/tex]