Question

ing Started Instruction Activity Erin Salo is taking this assessment. Multiple Choice Find all the real square roots of -(9)/(16). ( 1 point )

Answer 1

The real square roots of -(9)/(16) are ±(3)/(4).

Step-by-step explanation:

Calculation to find the real square roots of -(9)/(16).

Given expression: -(9)/(16)

To find the square root, we use the fact that the square root of a product is the product of the square roots:

`\[ √(-(9)/(16)) = √((-1) \cdot (9/16)) \]`

Now, we can break it down further:

`\[ √(-(9)/(16)) = √(-1) \cdot √((9/16)) \]`

The square root of -1 is denoted by 'i' in complex numbers. Therefore:

`\[ √(-(9)/(16)) = i \cdot (√(9)/√(16)) \]`

Now, simplify the square roots:

`\[ √(-(9)/(16)) = i \cdot (3/4) \]`

So, the complex square root of -(9)/(16) is
`\( i \cdot (3/4) \).` However, we are looking for real square roots, which means we need to consider both positive and negative values.
`\[ √(-(9)/(16)) = i \cdot (3/4) \]`

Therefore, the final real square roots are:

`\[ \pm i \cdot (3/4) \]`

In a real number context, 'i' represents the imaginary unit, but since we are looking for real square roots, we discard the 'i'. Thus, the final answer is:

`\[ \pm (3/4) \]`

This means that both ( (3/4) ) and ( -(3/4) ) are the real square roots of -(9)/(16), as squaring either of them results in the original expression.