Consider the following equation.

x^2 = 2

The equation above has_____ (A: two B: one C: three D: no) solution(s).
When x = , x is_____(A: Not a B: a) solution to the equation.
The solution(s) for the given equation are____ (A: rational B: irrational) number(s).

3 answers

Let's analyze the equation x2=2.

First, we can determine the number of solutions:

  1. Taking the square root of both sides, we get: x=2orx=2 Thus, there are two solutions: 2 and 2.

So, the equation above has (A: two) solution(s).

Next, when x=2 or x=2, we check if it is a solution:

  • Since both values satisfy the original equation x2=2, x=2 (and x=2) is (B: a) solution to the equation.

Finally, we need to determine the nature of the solutions:

  • Both 2 and 2 are not rational numbers (they cannot be expressed as a fraction of two integers). Therefore, the solutions for the given equation are (B: irrational) number(s).

Putting this all together:

  1. The equation above has (A: two) solution(s).
  2. When x=2, x is (B: a) solution to the equation.
  3. The solution(s) for the given equation are (B: irrational) number(s).
Simply square root of 16

The square root of 16 is 4.

This is because 4×4=16.

So, 16=4.