# Use rational exponents to write a single radical expression In other words, we need to find a square root. The principal square root is the nonnegative number that when multiplied by itself equals The square root obtained using a calculator is the principal square root.

### Rational exponents with variables

The principal square root of is written as The symbol is called a radical, the term under the symbol is called the radicand, and the entire expression is called a radical expression. To find out the length of ladder needed, we can draw a right triangle as shown in Figure , and use the Pythagorean Theorem. In other words, we need to find a square root. Rationalize denominators. Since the square root of is The square root function is the inverse of the squaring function just as subtraction is the inverse of addition. A hardware store sells ft ladders and ft ladders. So let me just write that down. Figure 1. To undo squaring, we take the square root. So it's a, b to the third power times the fourth root of 5. The principal square root of 25 is Evaluating Square Roots. So that's just a. So here we have the fourth root of 5 a to the fourth b to the twelfth power. The principal square root is the nonnegative number that when multiplied by itself equals The square root obtained using a calculator is the principal square root.

In this section students will: Evaluate square roots. Figure 1. In this section, we will investigate methods of finding solutions to problems such as this one.

In general terms, if is a positive real number, then the square root of is a number that, when multiplied by itself, gives The square root could be positive or negative because multiplying two negative numbers gives a positive number. Use rational roots.

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