To arrange the given expressions in descending order, we need to compare their values.
1. Let's simplify each expression:
- 2√3√5: This expression can be simplified as 2 times the square root of 3 times the square root of 5. We can multiply the square roots together to get the square root of the product of 3 and 5, which is the square root of 15. So, 2√3√5 becomes 2√15.
- 3√4√7: Similarly, this expression can be simplified as 3 times the square root of 4 times the square root of 7. The square root of 4 is 2, so 3√4√7 becomes 3 times 2 times the square root of 7, which is 6√7.
- √√3: This expression can be simplified by taking the square root of the square root of 3. The square root of 3 is approximately 1.732, so √√3 becomes √1.732.
2. Now, we can compare the simplified expressions:
- 6√7 is the largest expression since it has the highest numerical value.
- √1.732 is the next largest expression.
- 2√15 is the smallest expression since it has the lowest numerical value.
Therefore, the expressions arranged in descending order are:
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Verified answer
To arrange the given expressions in descending order, we need to compare their values.
1. Let's simplify each expression:
- 2√3√5: This expression can be simplified as 2 times the square root of 3 times the square root of 5. We can multiply the square roots together to get the square root of the product of 3 and 5, which is the square root of 15. So, 2√3√5 becomes 2√15.
- 3√4√7: Similarly, this expression can be simplified as 3 times the square root of 4 times the square root of 7. The square root of 4 is 2, so 3√4√7 becomes 3 times 2 times the square root of 7, which is 6√7.
- √√3: This expression can be simplified by taking the square root of the square root of 3. The square root of 3 is approximately 1.732, so √√3 becomes √1.732.
2. Now, we can compare the simplified expressions:
- 6√7 is the largest expression since it has the highest numerical value.
- √1.732 is the next largest expression.
- 2√15 is the smallest expression since it has the lowest numerical value.
Therefore, the expressions arranged in descending order are:
6√7, √1.732, 2√15