Evaluate :
`sqrt(5(2(3)/(4) - (3)/(10)))`

Answer

To evaluate the expression \( \sqrt{5 \left( 2 \left( \frac{3}{4} \right) - \frac{3}{10} \right)} \), we will follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{5 \left( 2 \left( \frac{3}{4} \right) - \frac{3}{10} \right)} \]

### Step 2: Calculate \( 2 \left( \frac{3}{4} \right) \)
To calculate \( 2 \left( \frac{3}{4} \right) \):
\[ 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \]

### Step 3: Substitute back into the expression
Now substitute \( \frac{3}{2} \) back into the expression:
\[ \sqrt{5 \left( \frac{3}{2} - \frac{3}{10} \right)} \]

### Step 4: Find a common denominator to subtract the fractions
The common denominator of \( 2 \) and \( 10 \) is \( 10 \). Convert \( \frac{3}{2} \) to have a denominator of \( 10 \):
\[ \frac{3}{2} = \frac{15}{10} \]
Now we can subtract:
\[ \frac{15}{10} - \frac{3}{10} = \frac{12}{10} = \frac{6}{5} \]

### Step 5: Substitute back into the expression
Now substitute \( \frac{6}{5} \) back into the expression:
\[ \sqrt{5 \left( \frac{6}{5} \right)} \]

### Step 6: Simplify the expression
Now simplify:
\[ \sqrt{5 \times \frac{6}{5}} = \sqrt{6} \]

### Step 7: Final result
The final result is:
\[ \sqrt{6} \]