How to Take the 4th Root of a Number

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A root of a number is a numerical value multiplied by itself a certain number of times that will equal the original number. If you have to find a fourth root of a number, it means that you must find a value that equals that number when it is multiplied by itself four times. You may have to find a fourth root as a part of a high school or college math or algebra course.

Things You'll Need

  • Calculator
  • Write down the number to which you must find a fourth root.

  • Write down an estimate as to what you think might equal this value when multiplied times itself four times. For example, if you have number 100, you might think of the number 5 as a fourth root.

  • Test your estimate by multiplying the number times itself four times. In this example, multiply 5 times 5 times 5 times 5, which equals 625. Obviously, this is no where near 100, so you will have to change your estimate accordingly.

  • Change and check your estimate until you arrive at the correct answer through the process of elimination. In this example, you might divide 5 in half to get 2.5. If you raise 2.5 to the fourth power, you get 39.0625, which is not enough. If you raise 3 to the fourth power, you get 81, which is closer. Because raising 4 to the fourth power would be 256, you know that the answer must be a little more than 3. In this case, you could continue this process until you arrive at the correct answer, which is 3.1622777.

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