Simplify. Remove all perfect squares from inside the square root. Assume x is positive. sqrt(54x^(7)) = ◻

Question

Bytelearn · Accepted Answer

Factor Perfect Squares: Factor the expression inside the square root to identify perfect squares. We need to factor 54x^7 into its prime factors and identify perfect squares. 54 can be factored into 2 * 3 * 3 * 3, and x^7 is already in prime form as x * x * x * x * x * x * x. So, sqrt(54x^7) = sqrt(2 * 3^3 * x^6 * x).Group Factors: Group the factors into perfect squares and separate the non-perfect squares. We have 3^3 which is 3^2 * 3, and x^6 which is (x^3)^2. These are our perfect squares. So, sqrt(54x^7) = sqrt(2 * 3^2 * x^6 * 3 * x).Take Square Roots: Take the square root of the perfect squares and leave the non-perfect squares inside the square root. The square root of 3^2 is 3, and the square root of x^6 is x^3. So, sqrt(54x^7) = 3 * x^3 * sqrt(2 * 3 * x).Simplify Expression: Simplify the expression inside the square root. We can't simplify sqrt(2 * 3 * x) any further because there are no more perfect squares. So, the final simplified expression is 3x^3 * sqrt(6x).

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $x$ is positive. $\newline$ $\sqrt{54 x^{7}}= \square$

Full solution

More problems from Simplify radical expressions with variables

Related topics

Simplify.\newlineRemove all perfect squares from inside the square root. Assume x x x is positive.\newline54x7=□\sqrt{54 x^{7}}= \square 54x7​=□

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $x$ is positive. $\newline$ $\sqrt{54 x^{7}}= \square$