Question $-9+\sqrt{-49}=$

Studdy Solution

STEP 1

What is this asking? We need to simplify an expression involving a negative number and the square root of a negative number. Watch out! Remember that the square root of a negative number involves imaginary numbers!

STEP 2

1. Simplify the square root
2. Combine the terms

STEP 3

Alright, let's rewrite that square root of a negative number using the imaginary unit $i$ .
Remember, $i$ is defined as $i = \sqrt{-1}$ , which is a super useful tool when dealing with square roots of negative numbers.
So, we can rewrite $\sqrt{-49}$ as $\sqrt{-1 \cdot 49}$ .

STEP 4

Now, we can split the square root: $\sqrt{-1 \cdot 49} = \sqrt{-1} \cdot \sqrt{49}$ .
Since $\sqrt{-1}$ is just $i$ and $\sqrt{49}$ is 7, this simplifies to $i \cdot 7$ , which we usually write as $7i$ .
So, $\sqrt{-49}$ simplifies to 7 $i$ !

STEP 5

Now, let's put it all together.
We started with $-9 + \sqrt{-49}$ .
We just figured out that $\sqrt{-49}$ is the same as $7i$ .
So, our expression becomes $-9 + 7i$ .

STEP 6

Since -9 and $7i$ are not like terms (one's a real number, and the other's an imaginary number!), we can't combine them any further.
That means $-9 + 7i$ is our final simplified form!

STEP 7

$-9 + 7i$

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