Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Absolutely, let's break down the original expression step by step:
The given expression is:
[tex]\[ 2 \sqrt{27} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12} \][/tex]
First, let's simplify each square root term individually:
1. \( \sqrt{27} \) can be simplified as:
[tex]\[ \sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3} \][/tex]
Therefore,
[tex]\[ 2 \sqrt{27} = 2 \cdot 3 \sqrt{3} = 6 \sqrt{3} \][/tex]
2. \( \sqrt{12} \) can be simplified as:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3} \][/tex]
3. Therefore:
[tex]\[ 2 \sqrt{12} = 2 \cdot 2 \sqrt{3} = 4 \sqrt{3} \][/tex]
Substituting these simplified terms back into the original expression, we get:
[tex]\[ 6 \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{3} - 4 \sqrt{3} \][/tex]
Now, let's combine like terms:
[tex]\[ 6 \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{3} - 4 \sqrt{3} \][/tex]
Combine coefficients of \( \sqrt{3} \):
[tex]\[ (6 + 2 - 3 - 4) \sqrt{3} = 1 \sqrt{3} \][/tex]
So, the simplified form of the expression is:
[tex]\[ \sqrt{3} \][/tex]
Thus, the correct choice is:
[tex]\[ \sqrt{3} \][/tex]
The given expression is:
[tex]\[ 2 \sqrt{27} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12} \][/tex]
First, let's simplify each square root term individually:
1. \( \sqrt{27} \) can be simplified as:
[tex]\[ \sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3} \][/tex]
Therefore,
[tex]\[ 2 \sqrt{27} = 2 \cdot 3 \sqrt{3} = 6 \sqrt{3} \][/tex]
2. \( \sqrt{12} \) can be simplified as:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3} \][/tex]
3. Therefore:
[tex]\[ 2 \sqrt{12} = 2 \cdot 2 \sqrt{3} = 4 \sqrt{3} \][/tex]
Substituting these simplified terms back into the original expression, we get:
[tex]\[ 6 \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{3} - 4 \sqrt{3} \][/tex]
Now, let's combine like terms:
[tex]\[ 6 \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{3} - 4 \sqrt{3} \][/tex]
Combine coefficients of \( \sqrt{3} \):
[tex]\[ (6 + 2 - 3 - 4) \sqrt{3} = 1 \sqrt{3} \][/tex]
So, the simplified form of the expression is:
[tex]\[ \sqrt{3} \][/tex]
Thus, the correct choice is:
[tex]\[ \sqrt{3} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.