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Combine the radicals [tex][tex]$5 \sqrt{27} - 17 \sqrt{3}$[/tex][/tex].

A. [tex][tex]$2 \sqrt{24}$[/tex][/tex]
B. [tex][tex]$28 \sqrt{3}$[/tex][/tex]
C. [tex][tex]$3 \sqrt{2}$[/tex][/tex]
D. [tex]-2 \sqrt{3}$[/tex]


Sagot :

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].
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