Answer :
Answer:152.531
Step-by-step explanation:
1. Start with the expression: \( 7 \sqrt{3} \sqrt{7} \sqrt{5} (7 - \sqrt{3} \sqrt{7} - \sqrt{5} - \sqrt{3} - 1) \sqrt{3} \)
2. Replace the square roots with their numerical values:
\( 7 \times 1.732 \times 2.646 \times 2.236 (7 - 1.732 \times 2.646 - 2.236 - 1.732 - 1) \times 1.732 \)
3. Calculate the products inside the parentheses:
\( (7 - 4.585 - 2.236 - 1.732 - 1) \)
4. Simplify the expression inside the parentheses:
\( (7 - 9.553) \)
5. Calculate the expression inside the parentheses:
\( -2.553 \)
6. Now, let's substitute this value back into the original expression:
\( 7 \times 1.732 \times 2.646 \times 2.236 \times (-2.553) \times 1.732 \)
7. Multiply all the numbers together:
\( \approx 152.531 \)
So, the value of the given expression is approximately \( 152.531 \) to three decimal places.
