Question

Which of the following operations could make the expression $x^2+\frac{8x}{\sqrt{3}}$ a perfect square?

• A. $Add(\frac{8}{\sqrt{3}}{)}^2$
• B. $Add(\frac{4}{\sqrt{3}}{)}^2$
• C. $Add(\frac{8}{3}x{)}^2$
• D. $Subtract\frac{8x}{\sqrt{3}}$

Answer 1

Answer: (B), (D)

The correct options are
B

$Add(\frac{4}{\sqrt{3}}{)}^2$

D

$Subtract\frac{8x}{\sqrt{3}}$

To make $x^2+\frac{8x}{\sqrt{3}}$ a perfect square, divide the co efficient of x by 2 and the add the square of the result to make this a perfect square.

Hence $\frac{8}{\sqrt{3}}÷2=\frac{4}{\sqrt{3}}$

Square of it is, $(\frac{4}{\sqrt{3}}{)}^2$

we should add $(\frac{4}{\sqrt{3}}{)}^2$ to make $x^2+\frac{8x}{\sqrt{3}}$ a perfect square.

Also,on subtraction of $\frac{8x}{\sqrt{3}}$ from the given expression , it will become $x^2$.

This operation also make the given expression a perfect square.