### About Solving Radical Equations Higher Roots:

We will often encounter radical equations with higher-level roots. These problems will mostly contain cube roots and fourth roots. Additionally, we may need to solve a radical equation that contains mixed roots. Solving this type of equation involves finding the LCM of the two indexes.

Test Objectives

- Demonstrate the ability to solve a radical equation with cube roots
- Demonstrate the ability to solve a radical equation with fourth roots
- Demonstrate the ability to solve a radical equation with mixed roots

#1:

Instructions: solve each equation.

$$a)\hspace{.2em}\large\sqrt[3]{2x - 2}=-2$$

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#2:

Instructions: solve each equation.

$$a)\hspace{.2em}\large\sqrt[4]{5x - 4}+ 5=7$$

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#3:

Instructions: solve each equation.

$$a)\hspace{.2em}\large\sqrt{5\sqrt{3x - 11}}=\sqrt{x + 11}$$

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#4:

Instructions: solve each equation.

$$a)\hspace{.2em}\large\sqrt{7\sqrt{6x + 9}}=\sqrt{5x + 3}$$

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#5:

Instructions: solve each equation.

$$a)\hspace{.2em}\large\sqrt{x + 1}=\sqrt[3]{4x - 5}$$

Note:

$$x^3 - 13x^2 + 43x - 24=(x - 8)(x^2 - 5x + 3)$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}x=-3$$

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#2:

Solutions:

$$a)\hspace{.2em}x=4$$

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#3:

Solutions:

$$a)\hspace{.2em}x=9,44$$

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#4:

Solutions:

$$a)\hspace{.2em}x=12$$

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#5:

Solutions:

$$a)\hspace{.2em}x=\frac{5 + \sqrt{13}}{2}, 8$$