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Select the correct answer.

What is this expression in simplified form?

[tex]\[ \sqrt{24} - 2 \sqrt{12} + 7 \sqrt{6} \][/tex]

A. [tex]\( 9 \sqrt{6} - 4 \sqrt{3} \)[/tex]
B. [tex]\( 7 \sqrt{6} \)[/tex]
C. [tex]\( 7 \sqrt{6} - 2 \sqrt{3} \)[/tex]
D. [tex]\( 15 \sqrt{2} \)[/tex]


Sagot :

To simplify the expression [tex]\(\sqrt{24} - 2 \sqrt{12} + 7 \sqrt{6}\)[/tex], let's break down the terms step-by-step.

1. First, simplify [tex]\(\sqrt{24}\)[/tex]:
[tex]\[ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \][/tex]

2. Next, simplify [tex]\(2 \sqrt{12}\)[/tex]:
[tex]\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \][/tex]
Thus,
[tex]\[ 2 \sqrt{12} = 2 \times 2 \sqrt{3} = 4 \sqrt{3} \][/tex]

3. The term [tex]\(7 \sqrt{6}\)[/tex] remains as is since it is already in its simplest form.

Now, we combine the simplified terms:
[tex]\[ 2 \sqrt{6} - 4 \sqrt{3} + 7 \sqrt{6} \][/tex]

Combine the like terms involving [tex]\(\sqrt{6}\)[/tex]:
[tex]\[ (2 \sqrt{6} + 7 \sqrt{6}) - 4 \sqrt{3} = 9 \sqrt{6} - 4 \sqrt{3} \][/tex]

So the expression in simplified form is:
[tex]\[ 7 \sqrt{6} - 2 \sqrt{3} \][/tex]

Among the given choices, the correct simplified form of the expression is:
[tex]\[ \boxed{7 \sqrt{6} - 2 \sqrt{3}} \][/tex]