State in each case whether true or false:
`3sqrt(7)-2sqrt(7)= sqrt(7)`

Answer

To determine whether the statement \(3\sqrt{7} - 2\sqrt{7} = \sqrt{7}\) is true or false, we can follow these steps:

### Step 1: Identify the expression on the left-hand side (LHS)
The left-hand side of the equation is \(3\sqrt{7} - 2\sqrt{7}\).

### Step 2: Factor out the common term
Both terms on the left-hand side have a common factor of \(\sqrt{7}\). We can factor it out:
\[ 3\sqrt{7} - 2\sqrt{7} = (3 - 2)\sqrt{7} \]

### Step 3: Simplify the expression
Now, we simplify the expression inside the parentheses:
\[ 3 - 2 = 1 \]
So, we have:
\[ (3 - 2)\sqrt{7} = 1\sqrt{7} \]

### Step 4: Write the simplified expression
This simplifies to:
\[ 1\sqrt{7} = \sqrt{7} \]

### Step 5: Compare with the right-hand side (RHS)
Now, we compare this with the right-hand side of the equation, which is \(\sqrt{7}\).

### Conclusion
Since both sides are equal:
\[ \sqrt{7} = \sqrt{7} \]
The statement \(3\sqrt{7} - 2\sqrt{7} = \sqrt{7}\) is **true**.

---