https://file.aiquickdraw.com/mathbot/file/1725452313037rf69hxm1.jpg

The expression in the image is:

\[
a = \sqrt{(3 - \sqrt{(6 - \sqrt{(10 + \sqrt{(15 + \sqrt{(21 - a)})})})})}
\]

This is an equation where \( a \) is defined in terms of itself through a nested square root expression. This type of equation is quite complex due to the recursive nature of \( a \). We can try to simplify or solve it by assuming a value for \( a \) and verifying if it satisfies the equation, or we can attempt to find an analytical solution.

### Solving the Equation:

To find a solution analytically, let's simplify the equation step by step.

1. Assume \( a \) is a specific value and substitute it into the expression.
2. Simplify the expression and compare it to the assumed value.

However, solving this directly might be very complex analytically. A common approach to handle such equations involves iterative approximation

Solve the nested square root expression involving constants: a = sqrt(3 - sqrt(6 - sqrt(10 + sqrt(15 + sqrt(21 - a)))))

Learn how to solve a complex nested square root expression: a = sqrt(3 - sqrt(6 - sqrt(10 + sqrt(15 + sqrt(21 - a))))) using algebraic concepts and recursion. Suitable for students in Grades 11-12.

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