Step-by-step explanation:

Let's solve this step by step.

Given:

1. \((a+b)^2 = 144\)

2. \(ab = 35\)

To find the value of \(a - b\), we can first expand \((a + b)^2\) using the formula for squaring a binomial:

\((a + b)^2 = a^2 + 2ab + b^2\)

Given that \((a + b)^2 = 144\), we can rewrite the equation:

\[a^2 + 2ab + b^2 = 144\]

Now substitute the value of \(ab = 35\) into the equation:

\[a^2 + 2 \times 35 + b^2 = 144\]

\[a^2 + 70 + b^2 = 144\]

From the equation \(ab = 35\), we can derive the equation \(a \times b = 35\). Given that \(ab = 35\), we know that \(a \times b = 35\).

Let's look at the equation \(a^2 + 70 + b^2 = 144\). We have \(a^2 + b^2 = 144 - 70\).

\[a^2 + b^2 = 74\]

Now, let's use the formula \((a - b)^2 = a^2 - 2ab + b^2\):

\((a - b)^2 = a^2 - 2ab + b^2\)

\((a - b)^2 = 74 - 2 \times 35\)

\((a - b)^2 = 74 - 70\)

\((a - b)^2 = 4\)

To find \(a - b\), take the square root of both sides of the equation:

\[a - b = \sqrt{4}\]

\[a - b = 2\]

Therefore, the value of \(a - b\) is \(2\).