# solving x^2=2^x with the super square root | Summary and Q&A

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November 9, 2019
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blackpenredpen
solving x^2=2^x with the super square root

## TL;DR

The video discusses the concept of the super square root and demonstrates its use in solving equations.

## Key Insights

• ✊ The super square root is a powerful concept that can be used in equations where the power moves to a different location.
• 🦸 The Lambert W function is a useful tool for calculating the super square root.
• 🦸 Equations involving the super square root may have real number solutions if a certain condition is met.

### Q: What is the super square root and when is it used?

The super square root is the X to the X power and is used when the power in an equation moves to a different location.

### Q: How do you calculate the super square root?

To calculate the super square root, you can use the Lambert W function. First, take the natural log of both sides of the equation, introduce the exponential function, and then apply the Lambert W function.

### Q: What is the condition for real number solutions in equations involving the super square root?

In equations involving the super square root, a must be greater than or equal to 1 divided by Euler's number, raised to the power of 1 over the super square root.

### Q: Can the super square root be used to solve equations with fractional powers?

Yes, the super square root can be used to solve equations with fractional powers. By raising both sides of the equation to the power of 1 over X, you can simplify the equation and solve for X.

## Summary & Key Takeaways

• The video introduces the concept of the super square root and explains that it can be used when the power in an equation moves to a different location.

• The super square root is defined as the X to the X power.

• The video demonstrates how to calculate the super square root using the Lambert W function and shows its application in solving equations.