If the denominator is a + b c, a + b c, then the conjugate is a − b c. įor a denominator containing the sum or difference of a rational and an irrational term, multiply the numerator and denominator by the conjugate of the denominator, which is found by changing the sign of the radical portion of the denominator. In other words, if the denominator is b c, b c, multiply by c c. To remove radicals from the denominators of fractions, multiply by the form of 1 that will eliminate the radical.įor a denominator containing a single term, multiply by the radical in the denominator over itself. We use this property of multiplication to change expressions that contain radicals in the denominator. We know that multiplying by 1 does not change the value of an expression. We can remove radicals from the denominators of fractions using a process called rationalizing the denominator. When an expression involving square root radicals is written in simplest form, it will not contain a radical in the denominator. The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression. The principal square root of a a is written as a. The square root obtained using a calculator is the principal square root. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root could be positive or negative because multiplying two negative numbers gives a positive number. In general terms, if a a is a positive real number, then the square root of a a is a number that, when multiplied by itself, gives a. To undo squaring, we take the square root. The square root function is the inverse of the squaring function just as subtraction is the inverse of addition. When the square root of a number is squared, the result is the original number. In this section, we will investigate methods of finding solutions to problems such as this one.

In other words, we need to find a square root. Now, we need to find out the length that, when squared, is 169, to determine which ladder to choose.

Simplify negative exponents