The value of 𝑍 is the square of the value of 𝑌. Circle the correct formula. Is it 𝑌 equals 𝑍 squared, 𝑍 equals two 𝑌, 𝑍 equals 𝑌 squared, or 𝑍 equals the square root of 𝑌.
As the question states, the value of 𝑍 is our formula must start 𝑍 equals. The word “is” in mathematics means equals. We’re told that 𝑍 is the square of 𝑌. Squaring something means multiplying it by itself. Therefore, 𝑍 is equal to 𝑌 multiplied by 𝑌. This can be written as 𝑍 is equal to 𝑌 squared. Any term multiplied by itself is the same as that term squared. If 𝑍 is the square of the value of 𝑌, the correct formula is 𝑍 equals 𝑌 squared.
The first incorrect answer has the variables the wrong way round. 𝑌 is equal to 𝑍 squared. This means that 𝑌 is the square of the value of 𝑍. The second incorrect answer states that 𝑍 is equal to two 𝑌. This means 𝑍 is equal to two multiplied by 𝑌. This would also be the simplified version of 𝑍 equals 𝑌 plus 𝑌 as 𝑌 plus 𝑌 is equal to two 𝑌. The third incorrect answer states that 𝑍 is equal to the square root of 𝑌.
The first and last formula are actually both the same. If we squared both sides of the last formula, we would get 𝑍 squared is equal to the square root of 𝑌 squared. As squaring and square rooting are inverse or the opposite of each other, the right-hand side just becomes 𝑌. This leaves us with 𝑌 is equal to 𝑍 squared, which is the same as the first formula.
None of these three answers are the correct formula if 𝑍 is the square of the value of 𝑌.