Question

Simplify the square root:square root of negative 72 end rootAnswer choices Include:2 i square root of 186 i square root of 218 i square root of 22 i square root of 6

Answer 1

The square root of negative 72 simplifies to 6i square root of 2. The process involves separating the negative component to produce an imaginary number and simplifying the square root of the positive component.

Step-by-step explanation:

To simplify the square root of negative 72, first recognize that the square root of a negative number is an imaginary number. Let's break this down step by step:

1. Write the negative number as a product of -1 and the positive number: -72 = -1 × 72.
2. Apply the square root to both factors separately, knowing that the square root of -1 is i, the imaginary unit.
3. Now, simplify the square root of 72. The number 72 can be factored into 36 × 2, and since 36 is a perfect square, √36 = 6.
4. The remaining square root operation is now simplified to 6√2.
5. Combine the imaginary unit with the simplified square root: 6i square root of 2.

Therefore, the square root of negative 72 is 6i square root of 2.

Answer 2

We need to simplify the next square root:

`\sqrt[]{-72}`

First, we need to rewrite the expression as:

`√(-72)=\sqrt[]{-1}\ast\sqrt[]{72}`

Where √-1 = i

Therefore:

`√(-1)\ast√(72)=\sqrt[]{72}\text{ i}`

Finally, we can simplify inside of the square root:

`\sqrt[]{72}i=√(6\ast6\ast2)i=√(6^2\ast2)i=6i\sqrt[]{2}^`

Therefore, the correct answer is "6 i square root of 2".