Chapter 6.6, Problem 96S

To determine

The value of the expression ${\left(2\sqrt{x}-5\right)}^2$ .

Answer to Problem 96S

The value of the expression ${\left(2\sqrt{x}-5\right)}^2$ is equal to $4x-20x^{\frac{1}{2}}+25$ .

Explanation of Solution

Given information: The given expression is,

  ${\left(2\sqrt{x}-5\right)}^2\mathrm{......}\left(1\right)$

Calculation: The given expression ${\left(2\sqrt{x}-5\right)}^2$ can be evaluated using (1) as,

  $\begin{array}{c}{\left(2\sqrt{x}-5\right)}^2={\left(2\sqrt{x}\right)}^2-\left(2\right)\left(2\sqrt{x}\right)\left(5\right)+{\left(5\right)}^2\\ =4x-20x^{\frac{1}{2}}+25\end{array}$