Yes, both of them are.
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The square root of 10 is an irrational number, because it continues endlessly and without pattern in decimal form.
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 10 is 3.162278
The square root of any positive real number (as in this case) is a real number. (Such square roots are usually irrational.)The square root of a negative real number, such as the square root of -15, is an imaginary, and therefore also a complex, number.