New Zealand
Level 7 - NCEA Level 2

Lesson

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=mx

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

1. Solve for $m$m.

2. Find the value of $\sqrt{m}+2$m+2 when $m=4$m=4.

3. Is $m=4$m=4 a solution of $\sqrt{m}+2=0$m+2=0?

Yes

A

No

B

Yes

A

No

B

##### QUESTION 3

Solve $\sqrt{2x+2}=\sqrt{4x+10}$2x+2=4x+10.

### Outcomes

#### M7-7

Form and use linear, quadratic, and simple trigonometric equations

#### 91257

Apply graphical methods in solving problems

#### 91261

Apply algebraic methods in solving problems