A Radical equation is the equation within a root. The root might be square root, cube root or any thing. There is no such formula for it but any radical equation can be solved by square or cubing or powering on both sides of the equation with nth power if it has n powers.

Lets illustrate this thing using a simple equation term $\sqrt[n]{x}$ - c = 0

$\sqrt[n]{x}$ - c = 0

Isolate the square root on any of the side of equation by shifting remaining term other side

$\sqrt[n]{x}$ = c

Raise both the sides by nth power

(x^{1/n})^{n} = c^{n}

x = c^{n}

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Given equation is $\sqrt{x}$ - 5 = 3 x

Isolate the root term to get

$\sqrt{x}$ = (3x - 5)

Squaring on both the sides to get

x = (3 x - 5)^{2}

x = 3 x^{2} + 25 - 30 x

31 x = 3 x^{2} + 25

3x^{2} - 31 x + 25 = 0

x = $\frac{ 31 x \pm \sqrt{31^2 - 900}}{6}$

Isolate the root term to get

$\sqrt{x}$ = (3x - 5)

Squaring on both the sides to get

x = (3 x - 5)

x = 3 x

31 x = 3 x

3x

x = $\frac{ 31 x \pm \sqrt{31^2 - 900}}{6}$

Given equation is $\sqrt[3]{x}$ - 8 = 0

Isolate the square root term to get

$\sqrt[3]{x}$ = 8

Cube the terms on both the sides to get

(x^{1/3})^{3} = 8^{3}

$\therefore$ x = 243