ANSWERS: 4
  • No, it would be a fourth root. 3 is the fourth root of 81, since 3^4 = 81. The square root of 81 is 9, and the square root of 9 is 3.
  • Fourth root.
  • Yes, you are right! It is quite obvious!
  • A fourth root. 1) The question should be: "What is a square root of a square root. Mathematically, we can only speak of *a* square root in the general case: "In mathematics, a square root of a number x is a number n such that n^2 = x, or, in other words, a number n whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root, which is denoted with a radical symbol as sqrt(x), or, using exponent notation, as x^(1/2). For example, the principal square root of 9 is 3, denoted sqrt(9)=3, because 3^2 = 3 × 3 = 9 and 3 is non-negative. The principal square root of a positive number, however, is only one of its two square roots. Every positive number x has two square roots. One of them is sqrt(x), which is positive, and the other -sqrt(x), which is negative. Together, these two roots are denoted ±sqrt(x). Square roots of negative numbers can be discussed within the framework of complex numbers." Source and further information: http://en.wikipedia.org/wiki/Square_root 2) The idea of a square root can be generalized with the n-th root. "In mathematics, a root of a number x is any number which, when repeatedly multiplied by itself, eventually yields x: In terms of exponentiation, r is a root of x if r×r×...×r=x for some positive integer n. For example, 2 is a root of 16 since 24 = 2 × 2 × 2 × 2 = 16. The number n is called the degree of the root. A root of degree 2 is called a square root, a root of degree 3 is called a cube root, a root of degree 4 is called a fourth root, and so forth. In general, a root of degree n is called an nth root." Source and further information: http://en.wikipedia.org/wiki/Nth_root 3) Now if f is a 4-th root of y, we have: y=f×f×f×f But we have also: y=(f×f)×(f×f) So that if x=(f×f) we can say: - f is a square root of x - x is a square root of y This show us that a fourth root is a square root of a square root.

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