Question

How is the missing number determined to make a perfect square?

Answer 1

Step-by-step explanation

a perfect square has the form

`a^2+2ab+b^2`

so, the thir t term would be

`\begin{gathered} b=(2ab)/(2√(a^2)) \\ √(thirterm)=\frac{second\text{ term}}{2*\sqrt{first\text{ term}}} \end{gathered}`

so

Step 1

`v^2+6v`
`v^2+6v\Rightarrow a^2+2ab`

hence

`\begin{gathered} √(b)=\frac{second\text{term}}{2\sqrt{first\text{ term}}} \\ √(b)=(6v)/(2√(v^2)) \\ √(b)=(6v)/(2v^) \\ √(b)=3 \\ √(b)=3 \\ b=3^2 \\ b=9 \end{gathered}`

therefore, the answer is

9

I hope this helps you