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How Do You Solve a Radical Equation?

Solve the equation 6√(2x) - 8 = 12 for x.

Summary

  1. The symbol above '2x' is a square root sign
  2. Solve for 'x' by getting it by itself on one side of the equation using the order of operations in reverse
  3. Get rid of the square root by squaring both sides
  4. Solve for 'x' by multiplying both sides by 1/2
  5. Check your answer by plugging it into the original equation and simplifying
  6. A true statement means the answer is correct!

Notes

    1. Solve for 'x' by getting it by itself on one side of the equation
    2. 'x' is a variable
    3. Since 'x' is under the radical, get the radical by itself first
    1. Adding 8 to both sides of the equation moves the 8 to the other side
    2. Dividing both sides of the equation by 6 cancels out the 6 on the left hand side
    3. Since both 20 and 6 are divisible by 2, 20/6 reduces to 10/3
    1. The radical is now isolated on one side of the equation
    2. The opposite of taking the square root of something is squaring it, or raising it to the power of 2
    3. So get rid of the square root by squaring both sides
    1. Get rid of the square root by squaring both sides
    2. Squaring and taking the square root are opposite operations, so they cancel each other out!
    3. When we square a fraction, we just square the numerator and denominator
    4. So (10/3)2 becomes 102/32, or 100/9
    1. We still have 2x on one side of the equation, but we want just 'x' by itself
    2. So we need to get rid of that 2 to solve for 'x'
    1. Since the right side of the equation is a fraction, it's easier to multiply both sides by 1/2
    1. Since there's a variable under the original radical, you must check your answer
    2. We can't take the square root of a negative numbers
    3. So we need to make sure the answer we got doesn't give us a negative under the radical!
    1. The value for 'x' could make the number under the square root a negative number
    2. We need to check and make sure that doesn't happen with the answer we got
    3. We can do this by plugging our value for 'x' into the original equation to see what happens
    1. Start from the inside and work your way out
    2. So first multiply the numbers under the square root, 2 times 50/9, to get 100/9
    3. Then take the square root of 100/9, which is 10/3
    4. Then we need to do any multiplication, so multiply 6 times 10/3 to get 20
    5. Now all we have left to do is subtract 20-8, which is equal to 12
    1. Plugging 50/9 in for 'x' and simplifying gives use a true statement
    2. That means the answer is correct!