Express in simplest radical form. sqrt(9x^(13)) sqrt(9x^(13)) 3sqrt(x^(13)) x^(6)sqrt(3x) 3x^(6)sqrtx

Break down square root: We start by breaking down the square root of the product into the product of square roots. √(9x^(13)) = √9 * √(x^(13))Simplify square root of 9: We know that the square root of 9 is 3 because 3^2 = 9. √9 = 3Simplify square root of x^(13): Next, we simplify the square root of x^(13). Since x^(13) = x^(12) * x, we can take the square root of x^(12) out of the radical because it is a perfect square (x^(6))^2 = x^(12). √(x^(13)) = √(x^(12) * x) = x^(6) * √xCombine results: Now we combine the results from the previous steps to get the simplest radical form. √(9x^(13)) = 3 * x^(6) * √x

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Math Problems

Calculus

Find indefinite integrals using the substitution

Full solution

Q. Express in simplest radical form.

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\sqrt{9 x^{13}}

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\sqrt{9 x^{13}}

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3 \sqrt{x^{13}}

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x^{6} \sqrt{3 x}

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3 x^{6} \sqrt{x}

Break down square root: We start by breaking down the square root of the product into the product of square roots. $\sqrt{9x^{13}} = \sqrt{9} \times \sqrt{x^{13}}$
Simplify square root of $9$ : We know that the square root of $9$ is $3$ because $3^2 = 9$ . $\newline$ $\sqrt{9} = 3$
Simplify square root of $x^{13}$ : Next, we simplify the square root of $x^{13}$ . Since $x^{13} = x^{12} \times x$ , we can take the square root of $x^{12}$ out of the radical because it is a perfect square $(x^{6})^2 = x^{12}$ . $\sqrt{x^{13}} = \sqrt{x^{12} \times x} = x^{6} \times \sqrt{x}$
Combine results: Now we combine the results from the previous steps to get the simplest radical form. $\sqrt{9x^{13}} = 3 \times x^{6} \times \sqrt{x}$