Any equation with a variable within a root is a radical equation. Radical formula helps in raising the powers of the left and right side of the equation until they come to the same value.

Radical equation can be any root, whether square or cube or some other root. Radical equation can be solved by squaring or cubing or powering both sides of equation with nth power. 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 n$^{th}$ power if it has n powers.

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

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

$\sqrt[n]{x}$ = c
Raise both the sides by nth power
(x1/n)n = cn
x = cn

### Solved Examples

Question: Solve the radical : $\sqrt[3]{x}=9$

Solution

Given,
$\sqrt[3]{x}=9$

$\left(x^{\frac{1}{3}}\right)^{3}=9$

x = 729

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