Question

find the s square root of the following by prime factorization method for 586756​

Answer 1

Given :

• Number = 586756

To Find :

• Square root by prime factorization.

Steps to be Followed :

1. Obtain the given number.
2. Resolve the given number into prime factors by successive division.
3. Make pairs of prime factors such that both the factors in each pair are equal.
4. Take one factor from each pair.
5. Find the product of the factors obtained in step 4.
6. The product obtained in step 5 is the required square root.

Solution :

Resolving 586756 into prime factors :

2 | 586756

2 | 293378

383 | 146689

383 | 383

| 1

Grouping the factors into pair :

⟶⠀586756 = (2 × 2) × (383 × 383)

Taking one factor from each pair :

⟶⠀√586756 = 2 × 383

⟶⠀√586756 = 766

So, Square Root of 586756 is 766

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