go step by step to reduse the radical ^48 plesae do it step by step
To simplify the square root of 48 step by step, we can break it down into prime factors:
1. Start by finding the prime factorization of 48.
48 = 2 * 2 * 2 * 2 * 3
2. Group the prime factors in pairs:
48 = (2*2) * (2*2) * 3
3. Simplify each group by taking the square root of the multiplied terms:
√48 = √(2*2) * √(2*2) * √3
4. Simplify the square roots:
√48 = 2 * 2 * √3
5. Multiply the numbers outside the square root:
√48 = 4√3
Therefore, the simplified form of √48 is 4√3.
To simplify the radical √48 step by step, you can follow these steps:
Step 1: Prime Factorization
Find the prime factors of 48:
48 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3
Step 2: Grouping the Factors
Group the factors in pairs and take out pairs of the same numbers from the square root:
√48 = √(2^4 × 3) = √(2^4) × √3
Step 3: Simplify the Pairs
Simplify the pairs that you took out from the square root:
√(2^4) = 2^2 = 4
Step 4: Final Simplification
Multiply the simplified pairs together and combine them with the remaining number outside the square root:
√(48) = 4√3
So, √48 is simplified to 4√3.
To simplify the radical √48, we can break it down into smaller factors and simplify the perfect squares.
Step 1: Start by factoring the number inside the square root to its prime factors:
48 = 2 x 2 x 2 x 2 x 3
Step 2: Group the prime factors into pairs. Since the square root involves pairs of numbers, we group them as follows:
48 = (2 x 2) x (2 x 2) x 3
Step 3: Simplify the perfect square pairs within the square root:
√48 = √(2 x 2) x √(2 x 2) x 3
Step 4: Simplify each pair separately:
√(2 x 2) = 2
√(2 x 2) = 2
Step 5: Combine the simplified pairs:
√48 = 2 x 2 x 3
Step 6: Multiply the simplified factors:
√48 = 2 x 2 x 3 = 4√3
Therefore, the simplified form of √48 is 4√3.