If x is the smallest number which is to be subtracted from 2605 to make it a perfect square, then the value of (4x+ 7) is :

The correct option is 23.

Step 1: Find the nearest perfect square less than 2605

We need to find the smallest number $x$ that must be subtracted from 2605 to get a perfect square.

Let's estimate the square root of 2605:

We know that:

${50}^2=2500$

${51}^2=2601$

${52}^2=2704$

Since 2605 is just greater than 2601 (${51}^2$), the largest perfect square less than or equal to 2605 is 2601.

Step 2: Calculate the value of $x$

To make 2605 a perfect square, we subtract $x$:

$2605-x=2601$

$x=2605-2601$

$x=4$

Step 3: Evaluate the expression $(4x+7)$

Now, substitute $x=4$ into the required expression:

$4x+7=4\left(4\right)+7$

$4x+7=16+7$

$4x+7=23$

Hence, the value of $(4x+7)$ is 23.