Q: Why does the square root of -25 have no real solution?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.

The square root of 8 over 25 is irrational, and real.

+25.

no. is not a real number

The principal root of a number is the positive real square root of the number - if it exists. Since -25 is negative, it does not have a real square root. Its square roots are the imaginary numbers +/-5i where i is the [imaginary] square root of -1. i is neither positive nor negative and so neither +5i nor -5i is a principal root.

Related questions

You can't take the square root of a negative number. The square root of -25 is 5i. It's an imaginary number.

the square root of 25 is 5

Yes. The square root of 25 is 5, which is a real number.

There is no real number [square] root of a negative number. There is a real cube root and a real fiftth root etc, but root, by itself, implies square root.

The square root of 8 over 25 is irrational, and real.

+25.

no. is not a real number

If by "radical" you mean "square root of", then yes. Both square roots of 25 are real numbers.

The principal root of a number is the positive real square root of the number - if it exists. Since -25 is negative, it does not have a real square root. Its square roots are the imaginary numbers +/-5i where i is the [imaginary] square root of -1. i is neither positive nor negative and so neither +5i nor -5i is a principal root.

You cannot in real numbers because the square of any number, negative or positive, is positive. However, -25 does have a square root in complex numbers: it is + or - 5i where i is the imaginary square root of -1.

The square root of 25 is 5 ... rational.

The square root of 25 is 5.