Solving a Radical Equation

Property A radical equation is one in which the variable appears under a square root or other radical. We solve simple radical equations by raising both sides to the appropriate power. To do this, first isolate the radical expression on one side of the equation. Then, raise both sides to the power that matches the index of the radical.

Examples To solve $3\sqrt{x 4}=15$, first divide by 3 to get $\sqrt{x 4}=5$. Square both sides: $(\sqrt{x 4})^2 = 5^2$, which gives $x 4=25$, so $x=29$. To solve $\sqrt[3]{y+1}+6=9$, first subtract 6 to get $\sqrt[3]{y+1}=3$. Then cube both sides: $(\sqrt[3]{y+1})^3 = 3^3$, which gives $y+1=27$, so $y=26$. Solve $2\sqrt{3x 2}=10$. Isolate the radical: $\sqrt{3x 2}=5$. Square both sides: $3x 2=25$. Solve for x: $3x=27$, so $x=9$.

Explanation Think of this as unwrapping a present; raising to a power is the inverse operation that undoes a root. Isolating the radical first ensures that this unwrapping process is clean and doesn't create a more complicated expression to solve.