Question

which choice is equivalent to the expression below?
√- 20
A. -20i
B. 2i √5
C. -2 √5
D. 2 √5i
E. 20i

Answer 1

\[\sqrt{-20} = \sqrt{ -1 * 4 * 5} = \sqrt{-1} \times \sqrt{4} \times \sqrt{5}\]

Answer 2

√-20 right ?

Answer 3

Simplify the right hand side.

No. sqrt(-20) is what is given and you have to simplify.
Look at the right hand side in my first reply.
What is sqrt(-1)?
What is sqrt(4)?

Answer 4

√4 is 2 and the √ of -1 and 5 were decimals

Answer 5

What is square root of -1?
sqrt(5) cannot be simplified and so leave it as it is.

Answer 6

i thought u couldnt find the sqaure root of -1 cause
its a negative

Answer 7

The symbol "i" is used to represent the square root of -1.

Answer 8

i tried to find it for -1 but its says that its invalid

Answer 9

You cannot use a calculator to find sqrt(-1).
sqrt(-1) = i
where "i" is a complex or imaginary number and not a real number.
i * i = i^2 = -1
i = sqrt(-1)

Answer 10

im not sure on how to find it

Answer 11

You just use the symbol "i" in the place of sqrt(-1).
You probably noticed "i" in some of your answer choices.

Answer 12

yes i have but i still don't understand this

Answer 13

Look at the right hand side of my first reply.
Replace sqrt(-1) with i
Replace sqrt(4) with 2
Leave sqrt(5) as is.
Multiply them all together. What do you get?

Answer 14

-40 ?

Answer 15

\[\sqrt{-20} = \sqrt{ -1 * 4 * 5} = \sqrt{-1} \times \sqrt{4} \times \sqrt{5} = i * 2 * \sqrt{5}\]

Answer 16

2i√5?

Answer 17

Yes.

Answer 18

so one is a imaginary number and the 5 and 4 came from the 20 ?

Answer 19

The letter "i" is an imaginary number not one.
1 on the right hand side of my first reply came form the negative sign which is equivalent to multiplying +20 and -1 which is -20.

Answer 20

For example, 12 = 4 * 3
-12 = -1 * 4 * 3

Answer 21

then u would look for the √ for them

Answer 22

If you are asked to simplify the square root of a number, try to find the factors of the numbers. If any of the factors is a perfect square, then you can easily take the square root of that number. The number 4 is a perfect square whose square root is 2.
9, 16, 25 are all perfect squares.
For example, Simplify sqrt(50)
sqrt(50) = sqrt(25 * 2) = sqrt(25) * sqrt(2) = 5*sqrt(2)

Simplify sqrt(-50)
sqrt(-50) = sqrt(-1 * 25 * 2) = sqrt(-1) * sqrt(25) * sqrt(2) = i * 5*sqrt(2) = 5isqrt(2)

Answer 23

wait, how do u knw wen a number is a real number ? like how do u tell ?

Answer 24

The numbers you are used to, positive numbers, negative numbers, zero, integers, rational numbers, irrational numbers are all real numbers. You can take the square root of any positive number and it will be a real number. But a square root of any negative number will be an imaginary number and square root of -1 has been assigned the symbol "i".

Answer 25

In the above example, square root of 50 is a real number: 5sqrt(2)
square root of (-50) is an imaginary (or complex number): 5isqrt(2)