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Assuming and are both positive, write the following expression in simplest radical form.Answer:
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Q. Assuming and are both positive, write the following expression in simplest radical form.Answer:
- Identify Perfect Square Factors: Identify the perfect square factors within the radical.We have the expression . The number is a perfect square, and we can also pair up the 's and 's into perfect squares. We can write as and as .
- Simplify Perfect Square Factors: Simplify the perfect square factors.Since is a perfect square, we can take the square root of , which is . For and , since both are perfect squares and , we can take the square root of each, which gives us and respectively.
- Pull Out Square Roots: Pull out the square roots of the perfect squares from the radical. We can now rewrite the expression as , since we have taken the square root of the perfect squares and left the non-perfect squares inside the radical.
- Multiply Constants and Variables: Multiply the constants and the variables outside the radical. Multiplying and gives us . We also multiply and together. The expression now is .
- Combine Square Roots: Combine the square roots inside the radical.Since both and are under a square root, we can combine them into a single square root. The expression now becomes .
