Solve the Square Root Equation: Finding X in √6x = √36

Video Solution

Solution Steps

00:06 Let's find the value of X.

00:09 First, we need to isolate X. This means getting X by itself in the equation.

00:18 Next, let's break down 36 into its factors: 6 times 6.

00:25 Remember, when multiplying the square root of a number A. By the square root of another number B.

00:31 The result is the square root of A times B. Together.

00:36 We'll apply this formula to our problem, and convert one square root to 2 for simplicity.

00:42 Now, simplify everything whenever possible.

00:46 And there you have it, this is our solution!

Step-by-Step Solution

To solve the equation $\sqrt{6}x = \sqrt{36}$ , we will proceed with the following steps:

Step 1: Simplify the square root on the right-hand side.
$\sqrt{36} = 6$ .
Step 2: Substitute the simplified value back into the equation to obtain:
$\sqrt{6}x = 6$ .
Step 3: Solve for $x$ by isolating the variable. Divide both sides by $\sqrt{6}$ :
$x = \frac{6}{\sqrt{6}}$ .
Step 4: Simplify the fraction:
Multiply the numerator and denominator by $\sqrt{6}$ :
$x = \frac{6 \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}} = \frac{6 \sqrt{6}}{6} = \sqrt{6}$ .

Therefore, the solution to the equation is $x = \sqrt{6}$ .