Question

Simplify 2√−50+√−72
Im having a bit of a hard time understanding how the answer to this problem is 16i√2
can someone explain?

Answer 1

Answer:

$16i\sqrt{2}$

Step-by-step explanation:

Given expression:

$2\sqrt{-50}+\sqrt{-72}$

Rewrite -50 as (25 · -2)  and -72 as (36 · -2)

$\implies 2\sqrt{25\cdot -2}+\sqrt{36 \cdot -2}$

$\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:$

$\implies 2\sqrt{25}\sqrt{-2}+\sqrt{36}\sqrt{-2}$

Rewrite 25 as 5² and 36 as 6²:

$\implies 2\sqrt{5^2}\sqrt{-2}+\sqrt{6^2}\sqrt{-2}$

$\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0$

$\implies 2 \cdot 5\sqrt{-2}+6\sqrt{-2}$

Simplify:

$\implies 10\sqrt{-2}+6\sqrt{-2}$

$\implies 16\sqrt{-2}$

$\textsf{Apply radical rule} \quad \sqrt{-a}=\sqrt{-1}\sqrt{a}:$

$\implies 16\sqrt{-1}\sqrt{2}$

$\textsf{Apply imaginary number rule}\quad \sqrt{-1}=i$

$\implies 16i\sqrt{2}$

Learn more about radical rules here:

https://brainly.com/question/28106222