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Assuming and are both positive, write the following expression in simplest radical form.
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Q. Assuming and are both positive, write the following expression in simplest radical form.
- Identify Perfect Squares: Let's first focus on the constant and the variables inside the radical separately.For the constant , we know that is a perfect square, so we can write it as .For the variables, we need to find the largest square factors. can be written as , and can be written as , where and are perfect squares.
- Rewrite Using Square Factors: Now we can rewrite the radical expression using these square factors: .
- Take Square Root of Perfect Squares: Next, we can take the square root of the perfect squares outside the radical: . We took from , from , and from .
- Combine Terms Outside Radical: Finally, we simplify the expression by combining the terms outside the radical:.This is the simplest radical form of the original expression.
