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lys-0071 [83]
3 years ago
5

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 <em>i, </em>and here is the thing it does that breaks the rules and makes it imaginary:

<em>i</em>²=-1

so

√-1=<em>i </em>

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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Step-by-step explanation:

For this case we have the following info given:

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