Express the following in simplest radical form. All variables represent positive real numbers.
square root of 80a^2b divided by the square root of7a^3b^7
I got an answer of 4 square root of 5 divided by b^3 square root of 7a
Looks like we got the same answer:
(4/b^3) * sqrt(5 / 7a).
The final answer should be under 1 radical.
To express the given expression in simplest radical form, you need to simplify the square roots individually and then divide them.
Let's start by simplifying the numerator, which is the square root of 80a^2b.
Since 80 can be factored as 8 * 10 and 8 can be simplified as 2 * 2 * 2, we can rewrite the square root of 80 as the square root of (2 * 2 * 2 * 10).
Taking out the perfect squares from under the square root, we can simplify it as 2 * 2 * square root of (2 * 10).
Simplifying it further, we have 4 * square root of (20).
Now let's simplify the denominator, which is the square root of 7a^3b^7.
We can rewrite the square root of 7a^3b^7 as the square root of (7 * a^2 * a * b^6 * b).
Taking out the perfect squares from under the square root, we can simplify it as a * b^3 * square root of (7ab).
Now, divide the numerator and denominator,
(4 * square root of (20)) / (a * b^3 * square root of (7ab))
Finally, you can rearrange the expression as follows for your answer:
4 * square root of 5 / b^3 * square root of (7a)