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3 years ago

Is -√15 an imaginary or irrational number?

Mathematics

2 answers:

Leno4ka [110]3 years ago

7 0

Hey there! I'm happy to help!

An irrational number is a real number that can't be written as a ratio of two other integers (non-fraction numbers) so a number like π or √2.

An imaginary number is one that breaks a mathematical rule so it can't necessarily exist as a real number. The main imaginary number is i, and here is the thing it does that breaks the rules and makes it imaginary:

i²=-1

√-1=i

We know that you cannot square a real number and have it be negative because a negative number can only be obtained by multiplying a positive and a negative number. This also shows us that there cannot be a square root of a negative number.

We have the number -√15. The placement of that negative sign is CRUCIAL! The square root of any positive integer is going to be a real number, but the square root of a negative number is nonexistent aka imaginary. √-15 would be an imaginary number, but we have -√15, which is the same thing as -1·√15. The negative sign is not inside the square root, which makes it not imaginary, so this is an irrational number. You can plug it into a calculator and it would be -3.872983346....

Have a wonderful day and keep on learning :)

Kazeer [188]3 years ago

6 0

Answer:

irrational

$\sqrt{-15}$ would be imaginary

Step-by-step explanation:

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Add up the equations doing so straight down

x + -x = 0x = 0 so the x terms go away

2y + 2y = 4y

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As a check, plug this solution into each equation to see if you get a true statement or not. Let's do so with the first equation

x+2y = -10

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and then the second equation

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2 years ago

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Step-by-step explanation:

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2. In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:

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The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...

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so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.

You don't actually have to do the rest of the multiplication in order to find the required answer.

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Comment on degree

The degree of a term is the exponent of the variable. If there is more than one variable, the degree of the term is the sum of their exponents. For example, the polynomial ...

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has three terms, each of degree 2.

If this example were one of your problems, it would be rejected as "not a polynomial in one variable," since two variables are involved.

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