What is the radical expression that is equivalent 27 1/5 ?
fifthroot(27)
To find the radical expression that is equivalent to 27 1/5, we first need to convert the mixed number 27 1/5 into an improper fraction.
To do this, we multiply the whole number (27) by the denominator of the fraction (5), and then add the numerator (1). This gives us:
27 * 5 + 1 = 135 + 1 = 136
So, 27 1/5 is equal to 136/5 as an improper fraction.
Now, we can express 136/5 as a radical expression. To do this, we need to determine the prime factorization of the numerator (136) and denominator (5).
The prime factorization of 136 is:
136 = 2 * 2 * 2 * 17
The prime factorization of 5 is:
5 = 5
Now, we can write the radical expression by putting the factors in a perfect square under the square root symbol:
√(136/5) = √((2 * 2 * 2 * 17)/(5))
Next, we look for pairs of identical factors that we can simplify. In this case, we have two pairs of identical factors:
√((2 * 2 * 2 * 17)/(5)) = √((2^2 * 2 * 17)/(5)) = √((2^2 * 2 * 17)/(5^1))
Now, we can simplify further by taking one factor from under the square root (2^2) and one factor out the square root (5^1):
√((2^2 * 2 * 17)/(5^1)) = (2 * √((2 * 17)/(5)))
Therefore, the radical expression equivalent to 27 1/5 is 2√(34/5).
To find the radical expression that is equivalent to 27 1/5, we can simplify the mixed number into an improper fraction first.
A mixed number is composed of a whole number and a fraction. In this case, 27 is the whole number and 1/5 is the fraction. To convert this into an improper fraction, we multiply the denominator (5) by the whole number (27) and add the numerator (1).
27 * 5 + 1 = 136 + 1 = 137
So, 27 1/5 is equivalent to the improper fraction 137/5.
To express this as a radical expression, we can take the square root of the numerator and the square root of the denominator separately, if the index is 2.
√(137/5) = √137/√5
The radical expression that is equivalent to 27 1/5 is √137/√5.