# A triple square root problem (Berkeley mini math tournament) | Summary and Q&A

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August 27, 2022
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blackpenredpen
A triple square root problem (Berkeley mini math tournament)

## TL;DR

A math problem involving a radical equation is solved by making observations and using variable substitutions, resulting in a quick and straightforward method to find the sum of distinct real solutions.

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### Q: What is the objective of the math problem presented in the video?

The objective is to compute the sum of the four distinct real solutions (x1, x2, x3, x4) of the given radical equation.

### Q: Why is it important to find a quick and efficient method to solve the problem?

In math competitions or time-limited situations, it is crucial to find the most efficient solution method to save time and increase chances of success.

### Q: How does the video suggest approaching the problem?

The video advises making observations about the similarities in the equation's inputs and factorizing on the variable, x, to simplify the equation.

### Q: How are variable substitutions used in solving the problem?

By substituting y for 20 - x, the equation can be restructured into a simpler form, allowing for easier calculation and comparison of solutions.

## Summary & Key Takeaways

• The video presents a math problem involving a radical equation with four distinct real solutions: x1, x2, x3, and x4.

• The goal is to find the sum of these solutions.

• By making observations, factoring, and using variable substitutions, a quick and efficient method is demonstrated to find the solution.