simplify √48
√48 = √(16 * 3) = √16 * √3 = 4√3
To simplify √48, we can find the largest perfect square that divides 48 and take its square root.
First, let's find the prime factorization of 48:
48 = 2 * 2 * 2 * 2 * 3
Now, we can pair the prime factors:
48 = 2^4 * 3^1
Next, we group the pairs of prime factors, taking one factor from each pair, and leave any remaining factors outside the square root:
√48 = √(2^2 * 2^2 * 3)
Simplifying under the square root:
√48 = 2 * 2 * √3
The simplified form of √48 is 4√3.
To simplify √48, we need to find the largest perfect square that divides 48.
First, let's find the prime factorization of 48:
48 = 2 * 2 * 2 * 2 * 3
Now, identify pairs of identical factors. We have four 2's, so we can group them together as one term raised to the power of 4:
48 = (2^4) * 3
Now, √48 is the same as √((2^4) * 3).
Since the square root (√) distributes over multiplication, we can simplify further:
√48 = √(2^4) * √3
√(2^4) is equal to 2 raised to the power of half of the exponent, so:
√(2^4) = 2^(4/2)
Simplifying the exponent:
2^(4/2) = 2^2
Therefore, √48 becomes:
√48 = 2^2 * √3
Finally, we can simplify further:
√48 = 4√3
So, √48 simplified is 4√3.