Write the expression in simplest form. 2sqrt(7x)*3sqrt(14x^(2))

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Write Expression: Write down the given expression. We are given the expression 2sqrt(7x) * 3sqrt(14x^(2)). We need to multiply these two square roots together.Apply Property: Apply the multiplication property of square roots. According to the multiplication property of square roots, sqrt(a) * sqrt(b) = sqrt(a * b). So, we can multiply the square roots together to get sqrt(7x) * sqrt(14x^(2)).Multiply Coefficients and Roots: Multiply the coefficients and the square roots separately. The coefficients are 2 and 3, and the square roots are sqrt(7x) and sqrt(14x^(2)). Multiplying the coefficients gives us 2 * 3 = 6. Multiplying the square roots gives us sqrt(7x * 14x^(2)).Simplify Inside Square Root: Simplify the expression inside the square root. We have sqrt(7x * 14x^(2)) which simplifies to sqrt(98x^(3)). This is because 7x * 14x^(2) = 98x^(3).Factor Out Perfect Squares: Factor out perfect squares from the square root. We notice that 98 is 49 * 2 and 49 is a perfect square (7^2). Also, x^(3) can be written as x^(2) * x, where x^(2) is a perfect square. So, we can rewrite sqrt(98x^(3)) as sqrt(49 * 2 * x^(2) * x).Take Square Root of Perfect Squares: Take the square root of the perfect squares. The square root of 49 is 7, and the square root of x^(2) is x. So, we can take these out of the square root to get 7x * sqrt(2 * x).Multiply by Coefficient: Multiply the result by the coefficient from Step 3. We have 6 * (7x * sqrt(2 * x)), which simplifies to 42x * sqrt(2 * x).

Write the expression in simplest form. $\newline$ $2 \sqrt{7 x} \cdot 3 \sqrt{14 x^{2}}$

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Write the expression in simplest form.\newline27x⋅314x2 2 \sqrt{7 x} \cdot 3 \sqrt{14 x^{2}} 27x​⋅314x2​

Write the expression in simplest form. $\newline$ $2 \sqrt{7 x} \cdot 3 \sqrt{14 x^{2}}$