change the radical √(3/8) into simplest form a/b sqrt(c)
√(3/8) = √3/(2√2) * √2/√2 = √6/4 = 1/4 √6
Sure, let me simplify that for you.
First, let's simplify the expression √(3/8).
Since 3/8 cannot be reduced further, we can rewrite it as (1/4) * √3.
Now, the expression becomes (1/4)√3.
So, the simplest form of √(3/8) is (1/4)√3.
To simplify the radical √(3/8), we need to simplify the numerator and the denominator separately.
First, let's simplify the numerator, which is 3.
Since 3 does not have any perfect square factors, it cannot be simplified further.
Next, let's simplify the denominator, which is 8.
We can factorize 8 as 2 * 2 * 2.
Out of these factors, we have a pair of 2's that can be taken out from under the square root, leaving us with 2.
Now, we can simplify the radical √(3/8) as follows:
√(3/8) = √(3) / √(8)
Since √(8) = 2√(2), we have:
√(3/8) = √(3) / (2√(2))
Finally, simplifying further, we can multiply the numerator and denominator by √(2) to get the simplest form:
√(3/8) = (√(3) / (2√(2))) * (√(2) / √(2))
This gives us:
√(3/8) = (√(3) * √(2)) / (2 * √(2))
Simplifying the numerator further:
√(3/8) = √(6) / (2 * √(2))
Therefore, the simplest form of √(3/8) is:
√(3/8) = √(6) / (2 * √(2))
To simplify the radical √(3/8), we need to simplify the numerator and the denominator separately.
Step 1: Simplifying the numerator.
√3 cannot be simplified further because 3 is a prime number.
Step 2: Simplifying the denominator.
We can simplify the fraction 8 by factoring it.
The prime factorization of 8 is 2 × 2 × 2, which can be written as 2^3.
Now, let's substitute the simplified values into the original radical:
√(3/8) = √(3)/(√8)
Since √8 can be written as √(2^3) = 2√2, the fraction becomes:
√(3/8) = √3/(2√2)
Now, to rationalize the denominator (removing the radical from the denominator), we need to multiply the numerator and the denominator by the conjugate of the denominator, which is the same expression with the opposite sign.
√(3/8) = √3/(2√2) * (2√2)/(2√2)
This simplifies to:
√(3/8) = (√3 * 2√2)/(2 * 2)
Multiplying the terms in the numerator gives:
√(3/8) = (2√3√2)/(4)
Simplifying further:
√(3/8) = (2√6)/4
And dividing both terms in the fraction by 2:
√(3/8) = √6/2
Therefore, the simplest form as a/b√c is:
√(3/8) = √6/2