Simplify: `sqrt(2.42)xxsqrt(2.88)`

Answer

To simplify the expression \( \sqrt{2.42} \times \sqrt{2.88} \), we can follow these steps:

### Step 1: Rewrite the square roots
We can rewrite the square roots of the decimals by eliminating the decimal points. To do this, we can multiply both numbers by 100 (which is \( 10^2 \)) to move the decimal places.

\[ \sqrt{2.42} = \sqrt{\frac{242}{100}} \quad \text{and} \quad \sqrt{2.88} = \sqrt{\frac{288}{100}} \]

### Step 2: Combine the square roots
Now we can combine the two square roots:

\[ \sqrt{2.42} \times \sqrt{2.88} = \sqrt{\frac{242}{100}} \times \sqrt{\frac{288}{100}} = \sqrt{\frac{242 \times 288}{100 \times 100}} = \frac{\sqrt{242 \times 288}}{100} \]

### Step 3: Factor the numbers under the square root
Next, we need to factor \( 242 \) and \( 288 \) to simplify the square root:

- \( 242 = 2 \times 121 = 2 \times 11^2 \)
- \( 288 = 2 \times 144 = 2 \times 12^2 \)

### Step 4: Substitute the factors back into the square root
Now we can substitute these factors back into our expression:

\[ \sqrt{242 \times 288} = \sqrt{(2 \times 11^2) \times (2 \times 12^2)} = \sqrt{2^2 \times 11^2 \times 12^2} = \sqrt{(2 \times 11 \times 12)^2} \]

### Step 5: Simplify the square root
Taking the square root of the squared term:

\[ \sqrt{(2 \times 11 \times 12)^2} = 2 \times 11 \times 12 \]

### Step 6: Calculate the product
Now we can calculate \( 2 \times 11 \times 12 \):

\[ 2 \times 11 = 22 \quad \text{and} \quad 22 \times 12 = 264 \]

### Step 7: Divide by 100
Finally, we divide by 100:

\[ \frac{264}{100} = 2.64 \]

### Final Answer
Thus, the simplified expression is:

\[ \sqrt{2.42} \times \sqrt{2.88} = 2.64 \]