Question

Determine whether the statement is true or false. If false, give a counterexample. If a2=225 , then a=15 .

Answer 1

The statement is true; if
`\(a^2 = 225\)`, then a = 15.

Step-by-step explanation:

The given statement is a quadratic equation where
`\(a^2 = 225\)`. Taking the square root of both sides gives
`\(a = \pm15\)`. However, when dealing with real numbers, the positive square root is considered. Therefore, a = 15 is a valid solution to the equation.

It's important to note that squaring both positive and negative values yields the same result. In this case, a = -15 is the other solution, but for the specific statement, a = 15 is the true and correct answer.

Quadratic equations and the importance of considering both positive and negative solutions, particularly when dealing with square roots. Understanding the properties of quadratic equations is fundamental in algebra and mathematical problem-solving.

Answer 2

Answer: True

Step-by-step explanation:

`15^(2)=225`