Solve the Nested Square Root: Finding √√4

Question

Solve the following exercise:

$\sqrt{\sqrt{4}}=$

00:00 Solve the following problem

00:03 A 'regular' root is of the order 2

00:10 We'll break down 4 into 2 squared

00:15 When we have a number (A) to the power of (B) under a root of the order (B)

00:18 The root and the power cancel each other out and the result equals number A

00:21 We'll apply this formula to our exercise

00:25 This is the solution

To solve the expression $\sqrt{\sqrt{4}}$ , we'll proceed with the following steps:

Step 1: Evaluate the inner square root.
The expression $\sqrt{4}$ simplifies to 2, because 2 squared is 4.
Step 2: Now evaluate the square root of 2.
Since the result from step 1 is 2, we need to find $\sqrt{2}$ . This is the prime representation of the result because 2 cannot be further simplified.

Therefore, the answer to the problem $\sqrt{\sqrt{4}}$ is $\sqrt{2}$ .

$\sqrt{2}$