What is the square root of 5929? (Please don’t cheat) 100 points!
The Correct Answer and Explanation is:
The square root of 5929 can be found through prime factorization. Let’s break it down:
Step 1: Find the prime factorization of 5929.
Start by dividing 5929 by the smallest prime numbers until you reach the prime factors:
- 5929 is not divisible by 2 (it’s odd).
- Check divisibility by 3: the sum of digits (5 + 9 + 2 + 9 = 25) is not divisible by 3.
- Check divisibility by 5: 5929 doesn’t end in 0 or 5, so it’s not divisible by 5.
- Check divisibility by 7: 5929÷7=847(exact division)5929 \div 7 = 847 \quad \text{(exact division)}5929÷7=847(exact division) Now, we know 5929 = 7 × 847.
Step 2: Prime factorize 847.
Repeat the process with 847:
- 847 is not divisible by 2 (it’s odd).
- Check divisibility by 3: the sum of digits (8 + 4 + 7 = 19) is not divisible by 3.
- Check divisibility by 7: 847÷7=121(exact division)847 \div 7 = 121 \quad \text{(exact division)}847÷7=121(exact division) So, 847 = 7 × 121.
Step 3: Prime factorize 121.
Now, factor 121:
- 121 is divisible by 11: 121÷11=11121 \div 11 = 11121÷11=11 So, 121 = 11 × 11.
Step 4: Final prime factorization.
Combining everything, we get:5929=7×7×11×11=(7×11)2=7725929 = 7 × 7 × 11 × 11 = (7 × 11)^2 = 77^25929=7×7×11×11=(7×11)2=772
Step 5: Find the square root.
The square root of 5929 is the number whose square gives 5929, so:5929=77\sqrt{5929} = 775929=77
Conclusion:
The square root of 5929 is 77. This method uses prime factorization, and we can see that 5929 is a perfect square of 77.
