Exponents represent how many times a number, called the base, should be multiplied by itself. For example, 6^3 is the same as 6 * 6 * 6. When solving an equation for a variable, isolating the variable requires eliminating terms by applying the term's opposite. For example, addition is the opposite of subtraction and multiplication is the opposite of division. The opposite of exponents are roots. The smallest root, or radical, is the square root, denoted by the symbol √.
- Skill level:
Solve a radical equation that contains a variable under a square root sign by eliminating the root using a squared exponent. Apply the exponent of 2 to both sides of the equation to keep it equivalent.
Solve the radical equation √(x + 3) = 5. Square both sides of the equation to eliminate the root: (√(x + 3)) = 5^2 becomes x + 3 = 25. Note that the exponent doesn't get applied to the terms on the left because the root and exponent simply cancel each other out.
Finish solving x + 3 = 25 by subtracting 3 from both sides: x = 22. Plug the answer back into the original equation to check: √(22 + 3) = 5 becomes √25 = 5, which is correct.
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