# How Are Radical Expressions & Rational Exponents Used in Real Life? ••• skynesher/E+/GettyImages

Have you ever wondered where and when you would use your school math skills in real life? A rational exponent is an exponent in the form of a fraction. Any expression that contains the square root of a number is a radical expression. Both have real world applications in fields like architecture, carpentry and masonry. Radical expressions are utilized in financial industries to calculate formulas for depreciation, home inflation and interest. Electrical engineers also use radical expressions for measurements and calculations. Biologists compare animal surface areas with radical exponents for size comparisons in scientific research.

## Rational Exponent Examples

In a rational exponent, the denominator, or bottom number, is the root. While the numerator, or top number, is the new exponent. In the following examples, the carrot symbol indicates that the right half is the exponent of the left. For example:

x ^ (1/2) = √x (square root of X)

x ^ (1/3) = 3√x (cube root of X)

A radical expression is any expression or equation that contains a square root. The square root symbol indicates that the number inside is a radical. The number inside that square root is called the radicand. Variable numbers can also be radical expressions. For example:

√x+y

√16

12+√x

√3*x²

## Real World Examples of Rational Exponents

The financial industry uses rational exponents to compute interest, depreciation and inflation in areas like home buying.

For example, to calculate the inflation of a home that increases in value from p1 to p2 over a period of n years, the annual rate of inflation (expressed as a decimal) is i = (p2/p1)^(1/n) -1.

To calculate compound interest, the formula is F = P (1+i)^n , where F is the future value and P is the present value, i is the interest rate and n is the number of years. If you wanted to calculate the compound interest on \$1,000 for 18 months at 5 percent, the formula would be F = 1000 (1+.05)^(3/2).

## Real World Examples of Radical Expressions

Radical expressions are common geometry and trigonometry especially when calculating triangles. In the fields of carpentry and masonry, triangles often come into play when designing or constructing buildings that require angle measurements.

The ratio of the sides of a 30°- 60°- 90° right triangle is 1:2:√3, and the ratio of the sides of a 45°- 45°- 90° right triangle is 1:1:√2.

Within the field of electrical engineering, the use of radical expressions has to do with determining how much electricity is flowing through circuits. One of the simplest formulas in electrical engineering is for voltage, V = √PR, where P is the power in watts and R is the resistance in the measurement of ohms.

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