what is the square root of 640
√640 =
The Correct Answer and Explanation is :
sqrt(640) = 25.298221281347036
To simplify the square root of 640, we begin by factoring 640 into its prime factors:
640 = 2 × 320 = 2 × 2 × 160 = 2 × 2 × 2 × 80 = 2 × 2 × 2 × 2 × 40 = 2 × 2 × 2 × 2 × 2 × 20 = 2 × 2 × 2 × 2 × 2 × 2 × 10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5.
This prime factorization reveals that 640 consists of seven factors of 2 and one factor of 5.
Next, we group the prime factors into pairs:
(2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 5.
Each pair of identical factors can be taken out of the square root as a single factor.
Therefore, the square root of 640 simplifies as follows:
√640 = √[(2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 5]
= 2 × 2 × 2 × 2 × √5
= 16√5.
Thus, the simplified form of √640 is 16√5.
To express this as a decimal, we approximate √5 ≈ 2.236.
Therefore, 16√5 ≈ 16 × 2.236 ≈ 35.776.
This approximation shows that √640 is approximately 35.776.
In summary, √640 simplifies to 16√5, which is approximately 35.776.