Solve the Nested Square Root: Finding √√4

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

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

2

Step-by-step solution

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

  • Step 1: Evaluate the inner square root.
    The expression 4\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 2\sqrt{2}. This is the prime representation of the result because 2 cannot be further simplified.

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

3

Final Answer

2 \sqrt{2}

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \sqrt[5]{\sqrt[3]{5}}= \)

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