Solve the Nested Square Root: Finding √√4

Question

Solve the following exercise:

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

00:06 Let's solve this math problem together.

00:09 A regular square root is also known as a root of order two.

00:16 We'll express four as two to the power of two.

00:21 When a number, let's call it A, is raised to the power B under a root of order B.

00:28 The root and the power cancel each other out, leaving us with the number A.

00:32 Let's use this rule in our exercise now.

00:36 And that's how we find 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 $\sqrt{2}$ .

$\sqrt{2}$