Find the square root of 128. (1 point)
4√2
√64×√2
2√4
8√2
8√2
To find the square root of 128, we can simplify it by breaking it down into its prime factors.
The prime factorization of 128 is 2^7.
Now, we can rewrite the square root of 128 as the square root of (2^7).
Next, we can split the square root of 2^7 into the square root of 2^6 multiplied by the square root of 2.
The square root of 2^6 can be simplified as 2^3, because when we divide the exponent by 2, we get 6/2 = 3.
Therefore, the square root of 2^6 is equal to 2^3, which is 8.
So, the answer is 8 multiplied by the square root of 2.
Thus, the correct option is 8√2.
To find the square root of 128, we can use the prime factorization method.
1. Start by finding the prime factors of 128.
Prime factors of 128: 2 × 2 × 2 × 2 × 2 × 2 × 2
2. Group the prime factors in pairs.
2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2) × (2 × 2) × (2 × 2)
3. Remove one number from each pair and write it outside the square root symbol.
√(2 × 2) × √(2 × 2) × √(2 × 2)
4. Simplify the square roots.
2 × 2 × 2 = 8
5. The simplified answer is 8√2.
Therefore, the square root of 128 is 8√2.