Yes. They are called surds. They are also complex.
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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.
A complex number for example. Complex numbers involve i, the imaginary square root of -1.
The square root of 100 is rational since it is not repeating.
There is no real number whose square root can be negative so there is no real solution. So mathematicians invented the imaginary number i with the property that i*i = -1 i is fundamental to complex numbers.
Complex numbers are numbers of the a + bi where a and b are real number and i is the imaginary square root of -1.