Q: Is the square root of 25 a real number?

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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.

Because the square root of -25 would be that number that, squared, would equal -25. No number, positive or negative, can result in a negative square. Since -25 is a negative number, no number, positive or negative, can be squared to equal -25.

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.

The square root of a positive number results in a positive number. For example, the square root of 25 is 5. * * * * * Not true! There are two real square roots for every positive number: one positive and one negative. -5 is as much a square root of 25 as +5 is. However, the positive root is the principal root and so is often presented as the only root.

Related questions

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.

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

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

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

Because the square root of -25 would be that number that, squared, would equal -25. No number, positive or negative, can result in a negative square. Since -25 is a negative number, no number, positive or negative, can be squared to equal -25.

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.

The square root of a positive number results in a positive number. For example, the square root of 25 is 5. * * * * * Not true! There are two real square roots for every positive number: one positive and one negative. -5 is as much a square root of 25 as +5 is. However, the positive root is the principal root and so is often presented as the only 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, which is a rational number.