Multiply Square Roots: Calculate √(2/4) × √(8/16)

Video Solution

Solution Steps

00:00 Solve the following problem

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

00:07 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 multiplication

00:15 Make sure to multiply numerator by numerator and denominator by denominator

00:31 Simplify wherever possible

00:38 The square root of a fraction (A divided by B)

00:41 Equals the square root of the numerator(A) divided by the square root of the denominator (B)

00:52 This is the solution

Step-by-Step Solution

To solve the given exercise, let's simplify each square root expression separately:

Step 1: Simplify $\sqrt{\frac{2}{4}}$ .

The fraction $\frac{2}{4}$ simplifies to $\frac{1}{2}$ . Thus, $\sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}}$ .
Step 2: Simplify $\sqrt{\frac{8}{16}}$ .

The fraction $\frac{8}{16}$ simplifies to $\frac{1}{2}$ . Thus, $\sqrt{\frac{8}{16}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}}$ .
Step 3: Multiply the results from Step 1 and Step 2.

$\sqrt{\frac{2}{4}} \cdot \sqrt{\frac{8}{16}} = \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} = \frac{1 \cdot 1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2}$ .

Therefore, the solution to the given expression is $\frac{1}{2}$ .