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**Square root √107 cannot be reduced, because it already is in its simplest form.**- All radicals are now simplified. The radicand no longer has any square factors.

- The square root of one hundred and seven √107 = 10.344080432789

- In mathematics, a square root of a number a is a number y such that y² = a, in other words, a number y whose square (the result of multiplying the number by itself, or y * y) is a. For example, 4 and -4 are square roots of 16 because 4² = (-4)² = 16.
- Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 ^ 3 = 9 and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.
- The justification for taking out the square root of any number is this theorem to help simplify √a*b = √a * √b. The square root of a number is equal to the number of the square roots of each factor.

A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. For example, 2 is the square root of 4, because 2x2=4. Only numbers bigger than or equal to zero have real square roots. A number bigger than zero has two square roots: one is positive (bigger than zero) and the other is negative (smaller than zero). For example, 4 has two square roots: 2 and -2. The only square root of zero is zero. A whole number with a square root that is also a whole number is called a perfect square. The square root radical is simplified or in its simplest form only when the radicand has no square factors left. A radical is also in simplest form when the radicand is not a fraction.