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How Do You Subtract Radicals with Like Radicands?

Subtract these radicals: 3√30z - 2√30z - 12√30z

Summary

  1. The symbol over '30z' is a square root sign
  2. Subtracting radicals is just like subtracting with variables
  3. Pretending each radical is a variable can help you see how to combine them
  4. Use the Distributive Property to factor 'x' out of the problem
  5. Factor out the square root of 30z the same way you would factor out a variable
  6. Combine the coefficients, 3-2-12, to get -11 in front of the radical

Notes

    1. Adding and subtracting radicals is just like adding and subtracting variables
    2. We don't actually add or subtract the numbers under the radicals
    3. Instead, we add or subtract the numbers in front of the radicals and leave the radicals as they are
    4. Think about it like combining like terms in a variable expression
    1. We can rewrite the problem using variables instead of radicals to make it easier to simplify
    1. Remember, variables are just symbols that represents numbers
    2. We can use 'x' to represent the square root of 30z
    3. Use the Distributive Property to factor 'x' out of the problem
    4. The coefficients are '3', '2', and '12'
    1. The radicand is the number under the square root sign
    2. Subtracting radicals is just like subtracting variables
    3. We must have like radicals in order to subtract them
    4. Like radicals have the same value under the square root
    1. Like radicals have the same value under the square root
    1. When the radicals are the same, we can just imagine that the radicals are variables and subtract the numbers in front of them
    1. We can subtract by factoring out the radical using the Distributive Property
    2. Then we can combine the coefficients
    3. Make sure that you keep the sign from in front of each coefficient when you combine them!
    4. So we have (3-2-12) out in front of the radical
    1. The coefficients are the numbers out in front of the radical
    1. 3-2-12 = -11
    1. Our problem is now fully simplified!
    1. The value underneath the square root sign is a 'radicand'
    2. Subtracting radicals is just like subtracting variables
    3. We must have like radicals in order to subtract
    4. Like radicals have the same value under the root symbol