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3 years ago

Simplify square root of -40

Mathematics

2 answers:

faltersainse [42]3 years ago

5 0

if you know complex numbers:

sqrt (-40)

sqrt(-1) * sqrt(40)

sqrt(-1) * sqrt(4) * sqrt(10)

i * 2 * sqrt(10)

2i *sqrt(10)

If you do not know complex numbers:

it cannot be simplified because it is negative

no real solution

s2008m [1.1K]3 years ago

5 0

Answer: 2i $\sqrt{10}$

Step-by-step explanation: To simplify the square root of -40, think of the square root of -40 as the square root of -1 × the square root of 40.

The square root of -1 can be represented by the imaginary number i. So we have i × the square root of 40 or i $\sqrt{40}$ .

Next, root 40 breaks down breaks down to 2 root 10. We can see this by setting up a factor tree for 40. 40 is 2 x 20, 20 is 2 x 10, and 10 is 2 x 5. We have a pair of 2's in our factor tree and we have 2 x 5 at the bottom.

So we have i x 2 root 10 or 2i $\sqrt{10}$ .

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Anika [276]

Hi there!

»»————-　★　————-««

I believe your answer is:

(0.286, 5.587)

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

I have graphed the two equations in a program. When graphed, the lines intersect at point (0.286, 5.587).
See the graph attached.

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

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