Question

i can calculate solutions to radical equations.
show all work!!!

1. solve each equation or explain why there is no solution.

a. \\(sqrt3{5x} = 2\\)

b. \\(sqrt{x + 4} = 3\\)

Explanation:

Step1: Cube both sides to eliminate root

$$(\sqrt[3]{5x})^3 = 2^3$$
$$5x = 8$$

Step2: Isolate x by dividing by 5

$$x = \frac{8}{5}$$
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Step1: Square both sides to eliminate root

$$(\sqrt{x+4})^2 = 3^2$$
$$x+4 = 9$$

Step2: Isolate x by subtracting 4

$$x = 9 - 4$$
$$x = 5$$

Answer:

a. $x = \frac{8}{5}$
b. $x = 5$