# Write an expression in radical form

And then we also know if we take the product of things, and then raise them to some exponent, that's the same thing as raising each of the terms in the product to the exponent first, or each of the things that we're taking the product of to that exponent, and then multiplying. For a denominator containing a single term, multiply by the radical in the denominator over itself. They are really more examples of rationalizing the denominator rather than simplification examples. When simplifying radicals, it is often easier to find the answer by first rewriting the radical with fractional exponents. Although, with that said, this one is really nothing more than an extension of the first example. Okay, we are now ready to take a look at some simplification examples illustrating the final two rules. Solution Begin by finding the conjugate of the denominator by writing the denominator and changing the sign.

To get rid of them we will use some of the multiplication ideas that we looked at above and the process of getting rid of the radicals in the denominator is called rationalizing the denominator. This book is licensed under a Creative Commons by-nc-sa 3.

See the license for more details, but that basically means you can share this book as long as you credit the author but see belowdon't make money from it, and do make it available to everyone else under the same terms. However, there is often an unspoken rule for simplification. Depending on the original expression, though, you may find the problem easier if you take the root first and then take the power, or you may want to take the power first.

Squaring and square rooting are inverse operations.

## Write the exponential expression using radicals

Consider passing it on:. Individually both of the radicals are in simplified form. For 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.

HowTo: Given an expression with a single square root radical term in the denominator, rationalize the denominator Multiply the numerator and denominator by the radical in the denominator. One undoes the other. For a denominator containing a single term, multiply by the radical in the denominator over itself. Squaring and square rooting are inverse operations.