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The image contains the following mathematical expression and problem in Bengali:

\[ \sqrt{y \sqrt{y}} = (y \sqrt{y})^{\frac{y}{y}} \]

The problem asks to find the value of \( y \).

Let's break this down:

1. The left-hand side is \( \sqrt{y \sqrt{y}} \), which simplifies to \( (y \sqrt{y})^{1/2} \).

2. The right-hand side is \( (y \sqrt{y})^{\frac{y}{y}} \), where \( \frac{y}{y} = 1 \). So, this simplifies to \( y \sqrt{y} \).

Thus, the equation becomes:

\[
(y \sqrt{y})^{1/2} = y \sqrt{y}
\]

Now, squaring both sides:

\[
y \sqrt{y} = (y \sqrt{y})^2
\]

Simplifying the right-hand side:

\[
y \sqrt{y} = y^2 \cdot y = y^3
\]

This gives the equation:

\[
y \sqrt{y} = y^3
\]

Now, divide both sides by \( y \) (assuming \( y \neq 0 \)):

\[
\sqrt{y} = y^2
\]

Square both sides:

\[
y = y^4
\]

This leads to the equation:

\[
y^4 - y = 0
\]

Factor the equation:

\[
y(y^3 - 1) = 0
\]

Thus, \( y = 0 \) or \( y^3 = 1 \). Since \( y = 0 \) doesn't satisfy the original equation, we focus on \( y^3 = 1 \), which gives:

\[
y = 1
\]

Therefore, the value of \( y \) is \( 1 \).

---

Would you like further explanation or additional steps clarified?

Here are 5 related questions:
1. What is the general method for solving radical equations like this one?
2. How does the equation \( y^3 = 1 \) lead to \( y = 1 \)?
3. Why can't \( y = 0 \) be a solution here?
4. How does squaring both sides affect the equality in radical equations?
5. Can there be more complex solutions for such equations under different assumptions?

**Tip**: Always verify your solution by substituting it back into the original equation.

যদি y√y = (y√y)^y/y হয়, তবে y এর মান কত?

Learn how to solve the radical equation y√y = (y√y)^y/y. This step-by-step solution includes key concepts like radical simplification and exponentiation. Ideal for students in Grades 9-12 studying advanced algebra.

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