Solve Nested Square Roots: √√49 × √√16 Multiplication Problem

Question

Complete the following exercise:

$\sqrt{\sqrt{49}}\cdot\sqrt{\sqrt{16}}=$

00:00 Solve the following problem

00:03 Break down 49 to 7 squared

00:11 Break down 16 to 4 squared

00:18 The square root of any number (A) squared cancels out the square

00:22 Let's apply this formula to our exercise and proceed to cancel out the squares:

00:35 Break down 4 to 2 squared

00:40 The square root cancels the square

00:45 This is the solution

To find the value of $\sqrt{\sqrt{49}} \cdot \sqrt{\sqrt{16}}$ , we will follow these steps:

Step 1: $\sqrt{\sqrt{49}}$
- Calculate $\sqrt{49} = 7$ .
- Therefore, $\sqrt{\sqrt{49}} = \sqrt{7}$ .

Step 2: $\sqrt{\sqrt{16}}$
- Calculate $\sqrt{16} = 4$ .
- Therefore, $\sqrt{\sqrt{16}} = \sqrt{4} = 2$ .

Step 3: Multiply the simplified results:
- Multiply $\sqrt{7}$ by $2$ .
- The product is $2 \cdot \sqrt{7} = 2\sqrt{7}$ .

Therefore, the value of $\sqrt{\sqrt{49}} \cdot \sqrt{\sqrt{16}}$ is $\mathbf{2\sqrt{7}}$ .

$2\sqrt{7}$