Solve for X: Simplifying √20·√5/x = 2√25 Equation

Question

Solve for x:

$\frac{\sqrt{20}\cdot\sqrt{5}}{x}=2\cdot\sqrt{25}$

00:00 Find the value X

00:03 Isolate X

00:28 When multiplying a square root of a number (A) by a square root of another number (B)

00:32 The result equals the square root of their product (A times B)

00:37 Apply this formula to our exercise and calculate the product

00:44 Break down 100 into 10 squared

00:48 Break down 25 into 5 squared

00:51 Every square root of a number (A) squared equals the number itself (A)

00:54 Apply this formula to our exercise and cancel out the squares

01:05 This is the solution

To solve the equation \< $\frac{\sqrt{20}\cdot\sqrt{5}}{x} = 2\cdot\sqrt{25}$ \>, follow these steps:

Step 1: Simplify the left-hand side.
- Use the product rule for roots: $\sqrt{20} \cdot \sqrt{5} = \sqrt{20 \cdot 5} = \sqrt{100}$ .
Step 2: Simplify $\sqrt{100}$ to get $10\.$
Step 3: Substitute and simplify the equation:
$\(\frac{10}{x} = 2 \cdot \sqrt{25}$ .
Step 4: Simplify the right-hand side:
$\sqrt{25} = 5$ so $2 \cdot 5 = 10$ .
Step 5: Equate both sides:
$\frac{10}{x} = 10$ .
Step 6: Solve for $x$ :
Multiply both sides by $x$ , then divide by 10:
$10 = 10x$ produces $x = 1$ .

Therefore, the solution to the problem is $\boldsymbol{x = 1}$ .

$1$