Simplify the following expression: -4√192x
Understand the Problem
The question asks to simplify the given expression, which involves a square root. We need to simplify the radical by finding perfect square factors of 192 and then simplify the expression.
Answer
$-32\sqrt{3x}$
Answer for screen readers
$-32\sqrt{3x}$
Steps to Solve
- Factor 192
Find the prime factorization of 192: $192 = 2^6 \cdot 3 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$
- Rewrite the expression
Rewrite the original expression by factoring out perfect squares from under the square root: $-4\sqrt{192x} = -4\sqrt{2^6 \cdot 3 \cdot x}$ $-4\sqrt{2^6 \cdot 3x} = -4\sqrt{(2^3)^2 \cdot 3x}$
- Simplify the square root
Simplify the square root by taking out the perfect square: $-4\sqrt{(2^3)^2 \cdot 3x} = -4 \cdot 2^3 \sqrt{3x}$ $-4 \cdot 8 \sqrt{3x}$
- Multiply the constants
Multiply the constants outside the square root: $-4 \cdot 8 \sqrt{3x} = -32\sqrt{3x}$
$-32\sqrt{3x}$
More Information
The simplified form of $-4\sqrt{192x}$ is $-32\sqrt{3x}$. We extracted the perfect square factors from 192 to simplify the radical.
Tips
A common mistake is not fully factoring the number inside the square root, leading to an incompletely simplified expression. Also, forgetting to multiply the constant outside the square root after extracting the square root is another common mistake.
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