Solve Radical Equations
Radical terms are terms that have a root sign, such as a square root or cube root. Some equations contain radical terms and, in this lesson, we are going to look at how to solve these kinds of equations.
The process is basically the same as solving "regular" linear equations. We can still use backtracking (that is, using the opposite operation) to solve equations. So how do we backtrack radical terms? We use exponents or powers.
Proof:
The fractional index law states: $x^{\frac{1}{m}}=\sqrt[m]{x}$x1m=m√x
The power of a power law states: $\left(x^m\right)^n=x^{mn}$(xm)n=xmn
So:
| $\left(\sqrt[m]{x}\right)^m$(m√x)m | $=$= | $\left(x^{\frac{1}{m}}\right)^m$(x1m)m |
| $=$= | $x^{\frac{m}{m}}$xmm | |
| $=$= | $x^1$x1 | |
| $=$= | $x$x |
Worked Examples
QUESTION 1
Solve $\sqrt{x}=\sqrt{13}$√x=√13.
QUESTION 2
$\sqrt{m}+2=0$√m+2=0
Solve for $m$m.
Find the value of $\sqrt{m}+2$√m+2 when $m=4$m=4.
Is $m=4$m=4 a solution of $\sqrt{m}+2=0$√m+2=0?
Yes
ANo
B
QUESTION 3
Solve $\sqrt{-5x+2}=\sqrt{-2x+8}$√−5x+2=√−2x+8.