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3 years ago

What is the principal square root of -4

Mathematics

1 answer:

devlian [24]3 years ago

6 0

Answer:

The principal square root of -4 is 2i.

Step-by-step explanation:

$\sqrt{-4}$ = 2i

We have the following steps to get the answer:

Applying radical rule $\sqrt{-a} =\sqrt{-1} \sqrt{a}$

We get $\sqrt{-4} =\sqrt{-1} \sqrt{4}$

As per imaginary rule we know that $\sqrt{-1}=i$

= $\sqrt{4} i$

Now $\sqrt{4} =2$

Hence, the answer is 2i.

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3 years ago

One maid can clean the house four times faster than another. Working together they can clean the entire house in 4 hours. How lo

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5 hours long would it take the faster maid cleaning alone.

What is a linear equation in math?

A linear equation only has one or two variables.
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Suppose, time taken by faster maid be x , hours.

So, time taken by slower maid ,

$x_{2} = 4x_{1}$ ( 4 time faster maid )

Now, time taken by both of the made together is given by ,

$( \frac{x_{1}x_{2} }{x_{1} + x_{2} } )$

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Learn more about linear equation

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8 0

1 year ago

Solve the following equation by factoring 2x^2-5x-12=0

Korolek [52]

Answer: x = 4 and x = -3/2

Procedure:

1) Given: 2x^2 - 5x - 12 = 0

2) Multiply both sides by : 2(2x^2) - 2(5x) - 2(12) = 0

3) Rearrange: (2x)^2 -5(2x) - 24 = 0

4) Notice that the common factor is (2x)

5) Set the parenthesis with the common factor inside:

(2x ) (2x ) =0

6) The first sign is the same sign of the second term of the trinomial, which is negative, the second sign is the product of the signs of the second and the third terms of the polynomial, which is (-)*(-) = + (positive)

(2x - )(2x + ) = 0

7) find two numbers that sum up - 5x and its product is -24.

- 8 + 3 = - 5
(-8)(+3) = -24

=> the numbers in the factors are -8 and +3

(2x - 8) (2x + 3) = 0

That is the factored equation. Now you can solve

8) a) 2x - 8 = 0 => 2x = 8 => x = 8/2 => x = 4

b) 2x + 3 = 0 => 2x = - 3 => x = - 3/2

Answer: the two solutions are x = 4 and x = -3/2

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3 years ago

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3 years ago