Answer :
To combine the radicals [tex]\(5 \sqrt{27}-17 \sqrt{3}\)[/tex], let's follow these steps:
1. Simplify the radicals:
- For [tex]\(5 \sqrt{27}\)[/tex]:
[tex]\[ 5 \sqrt{27} = 5 \sqrt{9 \cdot 3} = 5 \cdot \sqrt{9} \cdot \sqrt{3} = 5 \cdot 3 \sqrt{3} = 15 \sqrt{3} \][/tex]
- For [tex]\(-17 \sqrt{3}\)[/tex]:
[tex]\[ -17 \sqrt{3} \quad (\text{this is already simplified}) \][/tex]
2. Combine the like terms:
Now that both terms are expressed with [tex]\(\sqrt{3}\)[/tex], we can combine them:
[tex]\[ 15 \sqrt{3} - 17 \sqrt{3} \][/tex]
3. Perform the subtraction:
[tex]\[ 15 \sqrt{3} - 17 \sqrt{3} = (15 - 17) \sqrt{3} = -2 \sqrt{3} \][/tex]
Thus, the expression [tex]\(5 \sqrt{27}-17 \sqrt{3}\)[/tex] simplifies to [tex]\(\boxed{-2 \sqrt{3}}\)[/tex].
1. Simplify the radicals:
- For [tex]\(5 \sqrt{27}\)[/tex]:
[tex]\[ 5 \sqrt{27} = 5 \sqrt{9 \cdot 3} = 5 \cdot \sqrt{9} \cdot \sqrt{3} = 5 \cdot 3 \sqrt{3} = 15 \sqrt{3} \][/tex]
- For [tex]\(-17 \sqrt{3}\)[/tex]:
[tex]\[ -17 \sqrt{3} \quad (\text{this is already simplified}) \][/tex]
2. Combine the like terms:
Now that both terms are expressed with [tex]\(\sqrt{3}\)[/tex], we can combine them:
[tex]\[ 15 \sqrt{3} - 17 \sqrt{3} \][/tex]
3. Perform the subtraction:
[tex]\[ 15 \sqrt{3} - 17 \sqrt{3} = (15 - 17) \sqrt{3} = -2 \sqrt{3} \][/tex]
Thus, the expression [tex]\(5 \sqrt{27}-17 \sqrt{3}\)[/tex] simplifies to [tex]\(\boxed{-2 \sqrt{3}}\)[/tex].
