Find the square root of a number 5929 by Prime Factorisation Method. A. 77
The Correct Answer and Explanation is:
To find the square root of 592959295929 using the prime factorization method, we first need to express 592959295929 as a product of prime factors. Then, we can take the square root by pairing the prime factors.
Step 1: Prime Factorization
Start by dividing 592959295929 by the smallest prime number, which is 222. Since 592959295929 is an odd number, it is not divisible by 222. So, we move to the next prime number, which is 333.
- 5929÷35929 \div 35929÷3 does not give an integer, so we move to 555.
- 5929÷55929 \div 55929÷5 does not work either, so we try 777.
Dividing by 777:
5929÷7=8475929 \div 7 = 8475929÷7=847
Now, factor 847847847:
- 847÷7=121847 \div 7 = 121847÷7=121
So we now have:
5929=7×7×1215929 = 7 \times 7 \times 1215929=7×7×121
Next, factor 121121121:
- 121÷11=11121 \div 11 = 11121÷11=11
So, the full prime factorization of 592959295929 is:
5929=7×7×11×115929 = 7 \times 7 \times 11 \times 115929=7×7×11×11
Step 2: Grouping the Prime Factors
Now, group the prime factors into pairs:
5929=(7×7)×(11×11)5929 = (7 \times 7) \times (11 \times 11)5929=(7×7)×(11×11)
Step 3: Taking the Square Root
To find the square root, take one number from each pair:
- 5929=7×11=77\sqrt{5929} = 7 \times 11 = 775929=7×11=77
Final Answer:
The square root of 592959295929 is 77\boxed{77}77.
Explanation:
The prime factorization method works by breaking a number down into its prime factors, then pairing those factors. Each pair of the same prime number represents a square, and you can take one factor from each pair. The product of these factors gives the square root.
