2= squared
x2+y2+z2+36 then square rooted and then the number must be rational.
I need x y and z. I already used 10 8 and 5
To find values for x, y, and z such that the expression x^2 + y^2 + z^2 + 36 results in a rational square root, we can follow these steps:
Step 1: Start with the given expression: x^2 + y^2 + z^2 + 36.
Step 2: Square root the expression: √(x^2 + y^2 + z^2 + 36).
Step 3: Simplify the expression and make it rational: √(x^2 + y^2 + z^2 + 36) = rational.
Step 4: Substitute the known values of x, y, and z (in this case, x = 10, y = 8, z = 5) into the expression: √(10^2 + 8^2 + 5^2 + 36).
Step 5: Calculate the square root expression with the substituted values: √(100 + 64 + 25 + 36) = √(225 + 36) = √261.
At this point, we need to determine whether √261 is a rational number or not. A rational number is any number that can be written as a fraction, where the numerator and the denominator are both integers. To determine if √261 is rational, we need to check if it can be expressed as a fraction (i.e., a rational number) or not.
By calculating the square root of 261, we find that √261 ≈ 16.155494... (the decimal value is approximate).
Since √261 is not a perfect square and cannot be expressed as a fraction, it is an irrational number. Therefore, it is not possible to find specific values for x, y, and z that satisfy the given conditions and result in a rational square root.