\text{The value of}\sqrt{90+\sqrt{97+\sqrt{4+\sqrt{19+\sqrt{36}}}}}\text{is:}

The correct option is 10.

To find the value of the given expression, we simplify it step-by-step from the innermost square root outwards:

The original expression is:

$$\sqrt{90+\sqrt{97+\sqrt{4+\sqrt{19+\sqrt{36}}}}}$$

Step 1: Simplify the innermost square root
Calculate the square root of 36:

$$\sqrt{36}=6$$

Substitute this value back into the expression:

$$\sqrt{90+\sqrt{97+\sqrt{4+\sqrt{19+6}}}}$$

Step 2: Simplify the next innermost square root
Add the terms inside the square root and simplify:

$$\sqrt{19+6}=\sqrt{25}=5$$

Now the expression becomes:

$$\sqrt{90+\sqrt{97+\sqrt{4+5}}}$$

Step 3: Simplify the next level
Add the numbers and evaluate the root:

$$\sqrt{4+5}=\sqrt{9}=3$$

Substitute 3 back into the expression:

$$\sqrt{90+\sqrt{97+3}}$$

Step 4: Continue simplifying outwards
Find the square root of the sum:

$$\sqrt{97+3}=\sqrt{100}=10$$

Substitute 10 back into the expression:

$$\sqrt{90+10}$$

Step 5: Solve the final square root
Evaluate the final term:

$$\sqrt{100}=10$$

Therefore, the final value of the given expression is 10.