Express in simplest radical form.
start fraction, square root of, 40, end square root, divided by, 6, end fraction
6
40
To express the fraction in simplest radical form, we can simplify the square root term.
First, let's simplify the square root of 40. We can factor 40 as the product of its largest perfect square factor and the remaining factor: 40 = 4 * 10 = 4 * (2 * 5). Since 4 is a perfect square (2 * 2), we can take it out of the square root:
sqrt(40) = sqrt(4 * (2 * 5)) = sqrt(4) * sqrt(2 * 5) = 2 * sqrt(2 * 5) = 2 * sqrt(10).
Now, we can rewrite the fraction as:
sqrt(40) / 6 = (2 * sqrt(10)) / 6.
Since both 2 and 6 have a common factor of 2, we can simplify further:
(2 * sqrt(10)) / 6 = 2/2 * sqrt(10) / 6 = 1/3 * sqrt(10) = ( sqrt(10) ) / 3.
Therefore, the fraction ( sqrt(40) ) / 6 is equal to ( sqrt(10) ) / 3 in simplest radical form.
To express the fraction √40 / 6 in simplest radical form, we can simplify the numerator and denominator separately.
Starting with the numerator, we look for perfect square factors of 40. The largest perfect square factor of 40 is 4, which divides evenly into 40. Therefore, we can rewrite the numerator as √(4 * 10).
Simplifying the numerator further, we have √4 * √10, which is 2√10.
Next, we simplify the denominator. There are no perfect square factors of 6 other than 1 and 6 itself.
Putting it all together, the fraction √40 / 6 simplifies to (2√10) / 6.
To simplify further, we can divide both the numerator and denominator by the greatest common factor, which in this case is 2. This gives us:
(2√10) / 6 = √10 / 3
Therefore, the expression in simplest radical form is √10 / 3.
To express the fraction in simplest radical form, you need to simplify the given square root.
First, we'll simplify the square root of 40. To do this, we can find the perfect square factors of 40. The factors of 40 include 1, 2, 4, 5, 8, 10, 20, and 40. Since none of these factors are perfect squares, we cannot simplify the square root of 40 any further.
Therefore, the simplified expression is:
sqrt(40) / 6