If `x- sqrtx`=`20`, Find the value of `sqrt x`
A. 5 B. 6. C. 8 D. 7

Options

A. D
B. B
C. C
D. A

Answer

To solve the equation \( x - \sqrt{x} = 20 \) and find the value of \( \sqrt{x} \), we can follow these steps:

### Step 1: Substitute \( \sqrt{x} \) with a variable
Let \( u = \sqrt{x} \). Then, we can express \( x \) in terms of \( u \):
\[ x = u^2 \]
Now, substituting this into the original equation gives:
\[ u^2 - u = 20 \]

### Step 2: Rearrange the equation
Rearranging the equation leads to:
\[ u^2 - u - 20 = 0 \]

### Step 3: Factor the quadratic equation
Next, we need to factor the quadratic equation \( u^2 - u - 20 = 0 \). We look for two numbers that multiply to \(-20\) and add to \(-1\). The numbers \(-5\) and \(4\) work:
\[ (u - 5)(u + 4) = 0 \]

### Step 4: Solve for \( u \)
Setting each factor to zero gives us the possible solutions:
\[ u - 5 = 0 \quad \Rightarrow \quad u = 5 \]
\[ u + 4 = 0 \quad \Rightarrow \quad u = -4 \]

### Step 5: Determine the valid solution
Since \( u = \sqrt{x} \) and the square root cannot be negative, we discard \( u = -4 \). Thus, we have:
\[ u = 5 \]

### Conclusion
Therefore, the value of \( \sqrt{x} \) is:
\[ \sqrt{x} = 5 \]

### Final Answer
The correct option is **A. 5**.