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The square root of a number:
The square root of a given positive real number is defined as the number multiplied by itself, resulting in the given number.
Example:
The square root of \(64\) is \(8\).
That is, \(\sqrt{64} = \sqrt{8 \times 8} = \sqrt{8^2} = 8\)
The square root of a polynomial:
The square root of a polynomial \(p(x)\) is defined as an expression \(q(x)\), when multiplied with itself, results in the given number \(p(x)\).
That is, \(p(x) = q(x) \times q(x)\)
So, \(\sqrt{p(x)} = |q(x)|\) where \(|q(x)|\) is the absolute of \(q(x)\).
The square root of a polynomial can be determined using two methods.
They are:
1. Factorization method
2. Long division method
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