Simplify the radical expression. sqrt (12x^12) Write your answer in the form A, sqrt B, or Asqrt B, where A and B are constants or expressions in x. Use at most one radical in your answer, and at most one absolute value symbol in your expression for A. ______

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Simplify the radical expression.  sqrt (12x^12)        Write your answer in the form A, sqrt B, or Asqrt B, where A and B are constants or expressions in x. Use at most one radical in your answer, and at most one absolute value symbol in your expression for A.  ______

Bytelearn · Accepted Answer

Factorizing 12: First, we need to factor the number 12 into its prime factors to see if any of them can be taken out of the square root. 12 can be factored into 2 * 2 * 3, which is 2^2 * 3.Rewriting x^12: Next, we look at the variable part, x^12. Since the exponent is even, we can rewrite x^12 as (x^6)^2, which is a perfect square.Rewriting the expression: Now we can rewrite the original expression using these factors: sqrt(12x^12) = sqrt(2^2 * 3 * (x^6)^2).Taking the square root: We can take the square root of the perfect squares, which are 2^2 and (x^6)^2, and move them outside the square root. The square root of 2^2 is 2, and the square root of (x^6)^2 is x^6. So, we have 2x^6 * sqrt(3).Final simplified expression: The expression 2x^6 * sqrt(3) is already simplified and in the form Asqrt B, where A is 2x^6 and B is 3. There is no need for an absolute value symbol because x^6 is always non-negative.

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