`sqrt(6.05)xxsqrt(8.45)=`_______

Options

A. 6.95
B. 7.35
C. 7.55
D. 7.15

Answer

To solve the problem \( \sqrt{6.05} \times \sqrt{8.45} \), we can follow these steps:

### Step 1: Rewrite the square roots
We can express the square roots in a more manageable form by eliminating the decimals.

\[ \sqrt{6.05} = \sqrt{\frac{605}{100}} = \frac{\sqrt{605}}{10} \]
\[ \sqrt{8.45} = \sqrt{\frac{845}{100}} = \frac{\sqrt{845}}{10} \]

### Step 2: Multiply the square roots
Now, we can multiply the two square roots together:

\[ \sqrt{6.05} \times \sqrt{8.45} = \frac{\sqrt{605}}{10} \times \frac{\sqrt{845}}{10} = \frac{\sqrt{605 \times 845}}{100} \]

### Step 3: Calculate the product under the square root
Next, we need to calculate \( 605 \times 845 \).

\[ 605 \times 845 = 511225 \]

### Step 4: Substitute back into the equation
Now we can substitute this back into our expression:

\[ \sqrt{6.05} \times \sqrt{8.45} = \frac{\sqrt{511225}}{100} \]

### Step 5: Calculate the square root of 511225
Next, we need to find \( \sqrt{511225} \). To do this, we can make pairs of digits from the right:

- Pairing: 5 | 11 | 22 | 25
- The largest perfect square less than or equal to 5 is \( 2^2 = 4 \).
- The largest perfect square less than or equal to 51 is \( 7^2 = 49 \).
- The largest perfect square less than or equal to 511 is \( 22^2 = 484 \).
- The largest perfect square less than or equal to 5112 is \( 71^2 = 5041 \).
- The largest perfect square less than or equal to 51122 is \( 142^2 = 20164 \).

After calculating, we find that:

\[ \sqrt{511225} = 715 \]

### Step 6: Final calculation
Now we can substitute this back into our equation:

\[ \sqrt{6.05} \times \sqrt{8.45} = \frac{715}{100} = 7.15 \]

### Final Answer
Thus, the answer is:

\[ \sqrt{6.05} \times \sqrt{8.45} = 7.15 \]

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