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In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
A non-nested radical expression is said to be in simplified form if no factor of the radicand can be written as a power greater than or equal to the index; there are no fractions inside the radical sign; and there are no radicals in the denominator.
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A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.).
Radical 175 or radical wrong (非部) meaning "wrong" is one of the 9 Kangxi radicals (214 radicals in total) composed of 8 strokes. In the Kangxi Dictionary , there are 25 characters (out of 49,030) to be found under this radical .
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1]
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
Raising the decimal digits of 175 to the powers of successive integers produces 175 back again: 175 = 1 1 + 7 2 + 5 3. [1] 175 is a figurate number for a rhombic dodecahedron, the difference of two consecutive fourth powers: 175 = 4 4 − 3 4. [2] It is also a decagonal number and a decagonal pyramid number, the smallest number after 1 that has ...