Use the list of five irrational below to answer the questions
square root of 2, square root of 6, square root of 12, square root of 18, and square root of 24.
part a. choose two numbers whose product is rational. explain.
part b. choose two numbers whose product is irrational. explain.

Step-by-step explanation:

A: The root will be rational if the product of the numbers under the radicals is a perfect square. For this part, there are a couple of choices.

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B: The root will be irrational if the product of the numbers under the radicals is not a perfect square. For this part, there are many choices.

109 is the nearest whole number/final answer! : )

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1