Simplify -4 * sqrt(192x)
Understand the Problem
The question is asking to simplify the given radical expression. This involves factoring out perfect squares from under the square root.
Answer
$-32\sqrt{3x}$
Answer for screen readers
$-32\sqrt{3x}$
Steps to Solve
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Factor 192 Find the prime factorization of 192. $192 = 2 \times 96 = 2 \times 2 \times 48 = 2 \times 2 \times 2 \times 24 = 2 \times 2 \times 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^6 \times 3$.
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Rewrite the expression Rewrite the original expression $-4\sqrt{192x}$ using the prime factorization of 192. $-4\sqrt{192x} = -4\sqrt{2^6 \times 3 \times x}$.
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Simplify the square root Simplify the square root by taking out perfect squares. $-4\sqrt{2^6 \times 3 \times x} = -4\sqrt{(2^3)^2 \times 3 \times x} = -4 \times 2^3 \sqrt{3x} = -4 \times 8 \sqrt{3x}$.
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Final simplification Multiply the constants. $-4 \times 8 \sqrt{3x} = -32\sqrt{3x}$.
$-32\sqrt{3x}$
More Information
The simplified form of $-4\sqrt{192x}$ is $-32\sqrt{3x}$.
Tips
A common mistake is not completely factoring the number under the square root, leading to an incompletely simplified expression. Another common mistake is incorrectly simplifying the powers of the variables or constants.
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