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what is the square root of 6x multiplied by the sqare root of 3x squared

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When you multiply 2 "square root expressions", you can put the multiplication problem under 1 square root. So,

√(6x) * √(3x2) = √(6x)*(3x2)

Follow the normal rules to multiply the expression under the square root,


Now put this expression in simple radical form, if required, which means factoring out all the "perfect squares" from under the square root.

Factor 18 into 9*2 because 9 is a perfect square (3*3)

Factor x3 into x2 * x because x2 is a perfect square

√18x3 = √(9x2 * 2x) = √9x2 * √2x

√9x2 = 3x   (because 3*3=9, x*x = x2, so 3x * 3x = 9x2)

√9x2 * √2x = 3x * √2x, which can also be written 3x√2x