Simplify the Square Root: √(100x⁴/25x²) Step-by-Step Solution

Solve the following exercise:

$\sqrt{\frac{100x^4}{25x^2}}=$

Let's solve the problem by following these steps:

• Step 1: Simplify the fraction under the square root.
  The expression is $\frac{100x^4}{25x^2}$. We can simplify this by dealing with the coefficient and the variable separately:
• The numerical part: $\frac{100}{25} = 4$.
• The variable part: $\frac{x^4}{x^2} = x^{4-2} = x^2$, using the laws of exponents.

Thus, the simplified fraction is $4x^2$.

• Step 2: Apply the square root.
  We have $\sqrt{4x^2}$. We apply the square root to both terms:
• $\sqrt{4} = 2$, since 2 squared equals 4.
• $\sqrt{x^2} = x$, assuming $x$ is positive (or using the absolute value to ensure non-negativity, but the context suggests a straightforward approach).

Thus, $\sqrt{4x^2} = 2x$.

• Conclusion:

Therefore, the solution to the expression is $2x$.