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 √.

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.

• Exponents represent how many times a number, called the base, should be multiplied by itself.
• The smallest root, or radical, is the square root, denoted by the symbol √.
• Solve a radical equation that contains a variable under a square root sign by eliminating the root using a squared exponent.

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.
The passage provides an explanation of exponents and radicals, followed by a step-by-step example of solving a radical equation. It includes a specific mathematical question and its solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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 √.

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.

• Exponents represent how many times a number, called the base, should be multiplied by itself.
• The smallest root, or radical, is the square root, denoted by the symbol √.
• Solve a radical equation that contains a variable under a square root sign by eliminating the root using a squared exponent.

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.
user
The passage provides an explanation of exponents and radicals, followed by a step-by-step example of solving a radical equation. It includes a specific mathematical question and its solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER