Chapter 11.3, Problem 47WE

To determine

To find: The required expression value.

Answer to Problem 47WE

The value of the required expression is -8

Explanation of Solution

Given,

The given values are,

  $x=20,y=16$

The given expression is,

  $\sqrt{x^2-y^2}-{\left(\sqrt{x}\right)}^2$

Calculation:

Substitute the value of x and y in $\sqrt{x^2-y^2}-{\left(\sqrt{x}\right)}^2$

  $\begin{array}{c}\sqrt{x^2-y^2}-{\left(\sqrt{x}\right)}^2=\sqrt{x^2-y^2}-{\left(\sqrt{x}\right)}^2\\ =\sqrt{{20}^2-{16}^2}-{\left(\sqrt{20}\right)}^2\\ =\sqrt{400-256}-20\\ =\sqrt{144}-20\end{array}$

Solve further as,

  $\begin{array}{c}\sqrt{x^2-y^2}-{\left(\sqrt{x}\right)}^2=12-20\\ =-8\end{array}$

Thus, the value of the required expression is -8