Find the square root of 128.
2√4
√64 x √2
4√2
8√2
To find the square root of 128, we can simplify it by factoring out perfect squares.
128 can be factored as 64 x 2.
The square root of 64 is 8, and the square root of 2 remains under the radical.
So, the square root of 128 is 8√2.
To find the square root of 128, we can break it down into simpler terms using the prime factorization method.
Step 1: Find the prime factorization of 128.
128 = 2^7
Step 2: Group the factors into pairs, and take one factor from each pair.
128 = 2^3 x 2^3 x 2 = 2^6 x 2.
Step 3: Simplify the expression by taking the square root of each factor.
√(2^6 x 2) = √(2^6) x √2
Step 4: Simplify further by expressing the square root of 2^6.
√(2^6) = 2^3 = 8.
Step 5: Combine the simplified terms.
√128 = 8√2.
Therefore, the square root of 128 is 8√2.
To find the square root of 128, we can use the prime factorization method.
Step 1: Prime factorize the number 128:
128 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7
Step 2: Rewrite the number using pairs of identical factors:
128 = 2^3 x 2^3 x 2 = (2^3)^2 x 2
Step 3: Take the square root of each pair and simplify:
√(2^3)^2 x 2 = 2^3 x √2 = 8√2
Therefore, the square root of 128 is 8√2.