Solve for X: Simplifying √4·√5/√25 Equation Step-by-Step

Question

Solve for x:

$\frac{\sqrt{4}\cdot\sqrt{5}}{\sqrt{25}}=2x$

Video Solution

Solution Steps

00:00 Find the value X

00:03 When multiplying the square root of a number (A) by the square root of another number (B)

00:06 The result equals the square root of their product (A times B)

00:10 Apply this formula to our exercise and proceed to calculate the product

00:15 Let's break down 25 to 5 squared

00:18 Any square root of a number (A) squared equals the number itself (A)

00:25 Apply this formula to our exercise and cancel out the square

00:28 Isolate X

00:42 This is the solution

Step-by-Step Solution

To solve $\frac{\sqrt{4} \cdot \sqrt{5}}{\sqrt{25}} = 2x$ , we follow these steps:

Simplify $\sqrt{4}$ : The square root of 4 is 2.
Simplify $\sqrt{5}$ : $\sqrt{5}$ remains $\sqrt{5}$ .
Simplify $\sqrt{25}$ : The square root of 25 is 5.
Substitute these values back: $\frac{2 \cdot \sqrt{5}}{5} = 2x$ .
Write the expression: $\frac{2\sqrt{5}}{5} = 2x$ .
Divide both sides by 2 to solve for $x$ :

x = \frac{2\sqrt{5}}{5 \cdot 2} = \frac{\sqrt{5}}{5}

The simplified expression for $\sqrt{5}$ is equivalent to $\frac{\sqrt{20}}{10}$ , using $\sqrt{5} = \frac{\sqrt{20}}{2}$ since $\sqrt{20} = 2\sqrt{5}$ .

Therefore, the solution to the problem is $\boxed{\frac{\sqrt{20}}{10}}$ .

Answer

$x=\frac{\sqrt{20}}{10}$

Related Subjects

Question Types

Square Root Quotient Property: Solving the equation