Certainly! Let's simplify the expression step by step.
Given the expression:
[tex]\[ 9 \sqrt{32} + 5 \sqrt{50} \][/tex]
Step 1: Simplify each square root term separately.
First, simplify [tex]\(\sqrt{32}\)[/tex]:
[tex]\[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \][/tex]
Then multiply by 9:
[tex]\[ 9 \sqrt{32} = 9 \cdot 4 \sqrt{2} = 36 \sqrt{2} \][/tex]
Next, simplify [tex]\(\sqrt{50}\)[/tex]:
[tex]\[ \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5 \sqrt{2} \][/tex]
Then multiply by 5:
[tex]\[ 5 \sqrt{50} = 5 \cdot 5 \sqrt{2} = 25 \sqrt{2} \][/tex]
Step 2: Add the simplified radical terms.
Now, combine [tex]\(36 \sqrt{2}\)[/tex] and [tex]\(25 \sqrt{2}\)[/tex]:
[tex]\[ 36 \sqrt{2} + 25 \sqrt{2} \][/tex]
Since the terms are like terms (both contain [tex]\(\sqrt{2}\)[/tex]), you can add the coefficients:
[tex]\[ 36 \sqrt{2} + 25 \sqrt{2} = (36 + 25) \sqrt{2} = 61 \sqrt{2} \][/tex]
Therefore, the simplified answer is:
[tex]\[ 9 \sqrt{32} + 5 \sqrt{50} = 61 \sqrt{2} \][/tex]
