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Find the value to three decimal places o f7 √3√7 √5 7−√3√7−√5−√3−1√3 1.(Take√3=1.732,√5=2.236,√7=2.646,√15=3.873)

Sagot :

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.