The Nature of Roots Of a Quadratic Equation help me with these pls if you answer correctly i'll mark you as brainliest answer

Problem 1

Answers:

Real = sqrt(49), 5/6, 12.5, 8/12, 225, sqrt(24)/16, sqrt(32)

Not real = sqrt(-20)  and  sqrt(-16)/9

Explanation:

Anything involving a square root of a negative number will result in a non-real answer. Anything else is real.

Traditionally y = sqrt(x) has a domain of nonnegative numbers. If x >= 0, then y is some real number. If x < 0, then we'll need to use the imaginary number i = sqrt(-1).

Problem 2

Answers:  

Rational = sqrt(49), 5/8, 12.5, 8/12, and 225

Irrational = sqrt(24)/16, sqrt(32)

Explanation:

Ignore the non-real numbers. Focus solely on the real values.

A rational number is where we can write it as a ratio of two integers. An example is 5/8 since 5 and 8 are integers. The denominator can never be zero.

Decimal values that terminate can be written as a fraction. For instance, 12.5 = 125/10.

Square roots of perfect squares are also rational. For example sqrt(49) = 7 = 7/1

Something like sqrt(32) is not rational because we can't write it in the form p/q with p,q being integers. We say it is irrational.

Problem 3

Answers:

Perfect Squares = 225

Non-perfect squares = everything else

Explanation:

A perfect square is of the form x^2, where x is a positive integer.

The only perfect square listed is 225 because 225 = 15^2. Here x = 15.

Note: a perfect square is an integer itself.

Problem 4

As discussed earlier, rational numbers are fractions of integers. So we have something of the form p/q where p,q are integers and q is nonzero. An example of a rational number is p/q = 7/8 with p = 7 and q = 8.

Irrational numbers are ones that cannot be written as p/q. A famous example of an irrational number is pi = 3.14, but we could do something like sqrt(17) for instance as well. The stuff under the square root must be a non-perfect square.

Perfect squares are integers in the form x^2, with x being an integer also. A visual way to think of perfect squares is to think of a square with side length x, so its area is x^2. If x = 9, then its area is x^2 = 9^2 = 81, so 81 is a perfect square. We only consider whole number side lengths.