To solve the given expression [tex]\( 3 \sqrt{8} + 2 \sqrt{50} - 5 \sqrt{18} \)[/tex], we will break it down step-by-step and simplify each term separately.
### Step 1: Simplify [tex]\( 3 \sqrt{8} \)[/tex]
First, recall that [tex]\( \sqrt{8} \)[/tex] can be expressed in terms of its prime factors:
[tex]\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \sqrt{2} \][/tex]
Thus,
[tex]\[ 3 \sqrt{8} = 3 \times 2 \sqrt{2} = 6 \sqrt{2} \][/tex]
### Step 2: Simplify [tex]\( 2 \sqrt{50} \)[/tex]
Now, express [tex]\( \sqrt{50} \)[/tex] in terms of its prime factors:
[tex]\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \][/tex]
Thus,
[tex]\[ 2 \sqrt{50} = 2 \times 5 \sqrt{2} = 10 \sqrt{2} \][/tex]
### Step 3: Simplify [tex]\( -5 \sqrt{18} \)[/tex]
Express [tex]\( \sqrt{18} \)[/tex] in terms of its prime factors:
[tex]\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2} \][/tex]
Thus,
[tex]\[ -5 \sqrt{18} = -5 \times 3 \sqrt{2} = -15 \sqrt{2} \][/tex]
### Step 4: Combine the simplified terms
Now, let's add up all the simplified expressions:
[tex]\[ 6 \sqrt{2} + 10 \sqrt{2} - 15 \sqrt{2} \][/tex]
Combine the coefficients of [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ (6 + 10 - 15) \sqrt{2} = 1 \sqrt{2} = \sqrt{2} \][/tex]
Therefore, the simplified form of the expression [tex]\( 3 \sqrt{8} + 2 \sqrt{50} - 5 \sqrt{18} \)[/tex] is [tex]\( \sqrt{2} \)[/tex].
### Result
[tex]\[
\boxed{\sqrt{2}}
\][/tex]
