Simplify the following:
1) \(\sqrt[6]{(12x^2y^4)(4xy^9)(6x^3)(8x^6y^2)}\)
2) \(\sqrt[3]{15a^5b^7}\cdot\sqrt[3]{75a^2b^4}\)
3) \(\sqrt{\large{\frac{2}{5}}}\normalsize\div\sqrt[4]{9}\)
4) \(\Large\frac{4x^3y\sqrt[5]{3x^8y^7}}{\sqrt[5]{27x^2y^{22}}}\)
5) Find positive integer \(N\) so that \(\sqrt[4]{1800N}\) is the smallest possible positive integer.
6) Find the volume of the rectangular solid with the following dimensions.
\(l=\sqrt[3]{16}\ \ \ \ \ b=\sqrt[3]{12}\ \ \ \ h=\sqrt[3]{72}\)
1) \(\sqrt[6]{(12x^2y^4)(4xy^9)(6x^3)(8x^6y^2)}\)
2) \(\sqrt[3]{15a^5b^7}\cdot\sqrt[3]{75a^2b^4}\)
3) \(\sqrt{\large{\frac{2}{5}}}\normalsize\div\sqrt[4]{9}\)
4) \(\Large\frac{4x^3y\sqrt[5]{3x^8y^7}}{\sqrt[5]{27x^2y^{22}}}\)
5) Find positive integer \(N\) so that \(\sqrt[4]{1800N}\) is the smallest possible positive integer.
6) Find the volume of the rectangular solid with the following dimensions.
\(l=\sqrt[3]{16}\ \ \ \ \ b=\sqrt[3]{12}\ \ \ \ h=\sqrt[3]{72}\)
7) Rewrite the following expression as a single radical expression: \( \sqrt[3]{4} \cdot \sqrt[4]{2} \)
8) Solve for \(x \): \( \frac{ \sqrt{15} x}{\sqrt{2}}=\frac{\sqrt{30}}{4} \)
9) Is \( -\sqrt{3} \) a solution to the equation \( x^2 - x \sqrt{2} +2 = \frac{\sqrt{18}}{x} + 5 \) ?
10) Find the x and y intercepts of the line with equation \( \sqrt{5}x - \sqrt{3} y = 2 \sqrt{45} \)