Question
Simplify the imaginary number. \( 2 \sqrt{-112} \)
Ask by Cummings Chen. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(2\sqrt{-112}\) simplifies to \(8\sqrt{7}i\).
Solution
Calculate or simplify the expression \( 2\sqrt{-112} \).
Calculate the value by following steps:
- step0: Calculate:
\(2\sqrt{-112}\)
- step1: Simplify the root:
\(2\times 4\sqrt{7}\times i\)
- step2: Multiply the numbers:
\(8\sqrt{7}\times i\)
The simplified form of the imaginary number \(2\sqrt{-112}\) is \(8\sqrt{7}i\).
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To simplify \( 2 \sqrt{-112} \), first, we can rewrite the expression as \( 2 \sqrt{112} \cdot \sqrt{-1} \). Since \( \sqrt{-1} \) is denoted as \( i \), we have: \[ 2 \sqrt{-112} = 2 \sqrt{112} i \] Now, simplify \( \sqrt{112} \). We can factor it: \[ \sqrt{112} = \sqrt{16 \cdot 7} = \sqrt{16} \cdot \sqrt{7} = 4\sqrt{7} \] Now substituting back, we get: \[ 2 \sqrt{-112} = 2 \cdot 4\sqrt{7} i = 8\sqrt{7} i \] So, the simplified form of the imaginary number is: \[ 8\sqrt{7} i \]
