How can you make this 5x²√18xy + √72x⁵y - x²√2xy in its simplest form Radicals
Answers
Step-by-step explanation:
please refer to the attached file
Step-by-step explanation:
Simplest Radical Form
Before we can simplify radicals, we need to know some rules about them. These rules just follow on from what we learned in the first 2 sections in this chapter, Integral Exponents and Fractional Exponents.
Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.
Laws of Radicals
Let's take the positive case first.
n-th root of a Positive Number to the Power n
We met this idea in the last section, Fractional Exponents. Basically, finding the n-th root of a (positive) number is the opposite of raising the number to the power n, so they effectively cancel each other out. These 4 expressions have the same value:
The 2nd item in the equality above means:
"take the n-th root first, then raise the result to the power n"
The 3rd item means:
"raise a to the power n then find the n-th root of the result"
Both steps lead back to the a that we started with.
For the simple case where \displaystyle{n}={2}n=2, the following 4 expressions all have the same value:
The second item means: "Find the square root of \displaystyle{9}9 (answer: \displaystyle{3}3) then square it (answer \displaystyle{9}9)".
The 3rd item means: "Square \displaystyle{9}9 first (we get \displaystyle{81}81) then find the square root of the result (answer \displaystyle{9}9)".
In general we could write all this using fractional exponents as follows: