Question

Multiply (Assume all expressions appearing under a square root symbol represent nonnegative numbers)(√5 - 3)² =

Answer 1

Given:

$(\sqrt{y}\text{ -3\rparen}^2$

Required:

Multiply (Assume all expressions appearing under a square root symbol represent nonnegative numbers)

Explanation:

$\mathrm{Simplify}\:\left(\sqrt{y}-3\right)^2$

Apply perfect square formula we get

$\left(a-b\right)^2=a^2-2ab+b^2$

we place the value in this formula we get,

$\begin{gathered} =(\sqrt{y})^2+(3)^2-2.\sqrt{y}.3 \\ \\ ==\left(\sqrt{y}\right)^2-2\sqrt{y}\cdot\:3+3^2 \end{gathered}$$\begin{gathered} (\sqrt{y})^2=y \\ \\ -2\sqrt{y}\cdot\:3=-6\sqrt{y} \\ \\ 3^2=9 \end{gathered}$$=y-6\sqrt{y}+9$

Required answer:

$=y-6\sqrt{y}+9$