Home >> Science & Nature >> Numerology

How to Add Square Roots With Exponents

At first glance, adding square roots with exponents may appear to be a daunting task. Square roots are a number's value if it were to be multiplied by itself. For example, the square root of 4 is 2 (reverse of 2 x 2), while the square root of 2 is radical 2 (which is the way a square root is expressed if it doesn't produce a whole number). Exponents, meanwhile, are the effectively the opposite procedure: They involve increasing the value of a number by multiplying it by the exponent (for instance, 4 raised to the second power [also known as "squaring"] is 16; radical 2 squared is 2). However, by following the order of operations, adding square roots that have exponents is actually quite simple.

Things You'll Need

Pen
Paper
Calculator (optional)

Instructions

- 1
  Simplify any square roots that produce whole numbers. Whole numbers are numbers without decimals; thus numbers like 4, whose square root is 2, produces a whole number when under the radical. Leave square roots that do not produce whole numbers unsimplified.
- 2
  Simplify all exponents. Any number that has an exponent should be simplified. To simplify any exponent, simply multiply the number by itself the number of times that the exponent indicates (for example if it the number is "6" with an exponent of "3," multiply 6 three times [6 x 6 x 6] to get 216).
- 3
  Add your remaining numbers. Note that before you could not add exponents and square roots; however, once each term has had its exponent or square root simplified, the terms can be added. If you have an unsimplified square root because the term was not a whole number, you cannot add these radicals. You may, however, use the calculator to determine an approximation of that square root and add said approximation to the final sum.

Numerology