Question

Simplify the expression. Write your answer as a complex number. 2 times the square root of 25 plus the square root of negative 16 10 + 4i 10 − 4i 10 + 8i 10 − 8i

Answer 1

Answer:

10 + 4i  

Step-by-step explanation:

$\begin{array}{rcl}2\sqrt{25} + \sqrt{-16} & = & 2 \times 5 + \sqrt{(-1)(16)}\\& = & \mathbf{10 + 4i}\\\end{array}$

Answer 2

Answer:

A. $10+4i$

Step-by-step explanation:

We are asked to simplify the given expression $2\times \sqrt{25}+\sqrt{-16}$.

We will use imaginary unit 'i' to solve our given problem.

Write 25 as square of 5:

$2\times \sqrt{5^2}+\sqrt{-16}$

$2\times 5+\sqrt{-16}$

$10+\sqrt{-16}$

$10+\sqrt{-1\times 16}$

Substitute $i^2=-1$ in the expression:

$10+\sqrt{i^2\times 16}$

Write 16 as square of 4:

$10+\sqrt{i^2\times 4^2}$

$10+4i$

Therefore, the simplified form of our given expression would be $10+4i$.