go step by step to reduse the radical ^48
To simplify the radical √48, we can start by determining the factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
We notice that 16 is a perfect square factor of 48.
Therefore, we can rewrite the square root of 48 as the square root of 16 times the square root of 3.
Taking the square root of 16, we get 4.
Thus, we have: √48 = 4√3.
To simplify the square root of 48, follow these steps:
Step 1: Begin by finding the factors of 48. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Step 2: Find the largest perfect square that divides evenly into 48. The largest perfect square that divides evenly into 48 is 16, which is equal to 4 squared.
Step 3: Rewrite the square root of 48 as the square root of 16 times the square root of 3. This is possible because the square root of a product is equal to the product of the square roots.
Step 4: Simplify the square root of 16, which is equal to 4.
Step 5: Simplify the square root of 3. Since 3 is not a perfect square, the square root of 3 cannot be simplified further.
Step 6: Putting it all together, the square root of 48 can be simplified as 4 times the square root of 3, which can be written as 4√3.
Therefore, the simplified form of the square root of 48 is 4√3.
To simplify the radical expression √48, you can follow these steps:
Step 1: Prime factorization
Find the prime factorization of the number inside the radical (√48).
Prime factorization of 48:
48 = 2 * 2 * 2 * 2 * 3
Step 2: Grouping factors
Pair up the prime factors in groups of two, which will allow you to take them out of the radical as a single term.
√48 = √(2 * 2 * 2 * 2 * 3)
= √(2^2 * 2^2 * 3)
Step 3: Take out pairs of like factors
Since there are two pairs of 2's, you can take them out of the square root symbol as a single term.
√(2^2 * 2^2 * 3) = 2 * 2 * √3
= 4√3
Therefore, the simplified form of √48 is 4√3.
can you show step by step
Apologies for the oversight. Here's a step-by-step breakdown:
Step 1: Prime factorization
Find the prime factorization of the number inside the radical (√48).
48 = 2 * 2 * 2 * 2 * 3.
Step 2: Grouping factors
Pair up the prime factors in groups of two, which will allow you to take them out of the radical as a single term.
√48 = √(2 * 2 * 2 * 2 * 3).
Step 3: Take out pairs of like factors
Since there are two pairs of 2's, you can take them out of the square root symbol as a single term.
√(2^2 * 2^2 * 3) = 2 * 2 * √3.
Step 4: Simplify the square root expression
Multiply the terms outside of the square root symbol, which gives you the simplified form of the expression.
2 * 2 * √3 = 4√3.
Therefore, the simplified form of √48 is 4√3.