An equation with a cube or square root is known as a radical formula. A radical formulation helps to lift the powers of the equation left and right side until they hit the same value.
Any root, whether square or cube or any other root can be solved by squaring or cubing or powering both sides of the equation with nth power. Squaring or cubing or powering both sides of the equation with nth, will solve a radical equation. Actually there no formula for the radical equation to solve it but if it has n power then powering two sides by n
\(\begin{array}{l}^{th}\end{array} \)
power gives the solution.Let us consider an equation
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\(\begin{array}{l}\sqrt[n]{x}\end{array} \)
– c = 0Isolate the square root on any of the sides of the equation by shifting remaining term other sides
\(\begin{array}{l}\sqrt[n]{x}\end{array} \) = c
Raise both the sides by nth power
(x1/n)n = cn
x = cn
Solved Example
Question:
Solve the radical : \(\begin{array}{l}\sqrt[3]{x}=9\end{array} \)
Solution
Given
\(\begin{array}{l}\sqrt[3]{x}=9\end{array} \)
\(\begin{array}{l}\left(x^{\frac{1}{3}}\right)^{3}=9^{3}\end{array} \)
x = 729
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