Question

Give examples of quadratic equation that can be solved by extracting the root with

Answer 1

Examples are given below.

Explanation:

Before solving the question, we should know the meaning of extracting the root.

Extracting the roots means isolating the square from the quadratic equation and after that applying the square root on both sides.

1. Example 1:

Consider a quadratic equation, $x^2-16=0$.

Step 1: Isolate the square from the quadratic equation.

$\Rightarrow x^2-16=0$

$\Rightarrow x^2=16$

Step  2: Apply the square root on both sides.

$\Rightarrow \sqrt{x^2}=\sqrt{16}$

$\Rightarrow |x|=\sqrt{16}$

We know that, $\sqrt{16}$ is equal to $4$.

$\Rightarrow |x|=4$

$\Rightarrow x=\pm4$

$\Rightarrow x=4,-4$

2. Example 2:

Consider a quadratic equation, $x^2-9=0$.

Step 1: Isolate the square from the quadratic equation.

$\Rightarrow x^2-9=0$

$\Rightarrow x^2=9$

Step  2: Apply the square root on both sides.

$\Rightarrow \sqrt{x^2}=\sqrt{9}$

$\Rightarrow |x|=\sqrt{9}$

We know that, $\sqrt{9}$ is equal to $3$.

$\Rightarrow |x|=3$

$\Rightarrow x=\pm3$

$\Rightarrow x=3,-3$

3. Example 3:

Consider a quadratic equation, $x^2-5=0$.

Step 1: Isolate the square from the quadratic equation.

$\Rightarrow x^2-5=0$

$\Rightarrow x^2=5$

Step  2: Apply the square root on both sides.

$\Rightarrow \sqrt{x^2}=\sqrt{5}$

$\Rightarrow |x|=\sqrt{5}$

$\Rightarrow x=\pm\sqrt{5}$

$\Rightarrow x=\sqrt{5},-\sqrt{5}$