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How do I simplify radicals in simplest radical form?

User Balloneij
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2 Answers

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28 votes

Final answer:

To simplify radicals, identify the largest square factor, simplify the components, and check your work for reasonableness. Use a calculator for complex or higher-order roots, and seek instructor guidance if needed.

Step-by-step explanation:

To simplify radicals in simplest radical form, you typically follow several steps. First, identify the largest square factor of the number under the radical. Then, you separate the number into its square factor and the remaining factor. If you have a square root of a number, such as \( \sqrt{18} \), you can break this down into \( \sqrt{9 \times 2} \), which simplifies to \( 3\sqrt{2} \) - because \( \sqrt{9} \) equals 3. In simplifying radicals, it's important to eliminate terms wherever possible to simplify the algebra.

When dealing with exponential radicals, like \( 10^{1.6} \), you would work to make the exponent an even number to facilitate taking the square root. This is done by adjusting the exponent such that the power of 10 (or any base) is evenly divisible by 2. The new square root can then be calculated by taking the square root of the digit term and halving the exponential term.

Always check the answer to ensure it is reasonable. Complex radicals or those with higher roots may require a calculator. When using square roots in equilibrium problems, mastering the simplification process is crucial. Always ask your instructor if you're not sure how to perform these operations.

User DannyK
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10 votes
10 votes

Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c

Examples of radicals are


\sqrt[]{4},\sqrt[2]{8},\sqrt[3]{16}

For exmaple,

Given the radical


\sqrt[]{12}

To simplify into the simplest radical,

Factorize the perfect square


\sqrt[]{12}=\sqrt[]{4*3}

Then we take out the pairs


\begin{gathered} \sqrt[]{12}=\sqrt[]{4}*\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2*2}*\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2^2}*\sqrt[]{3} \end{gathered}

Simplify the result


\begin{gathered} \text{Where} \\ \sqrt[]{2^2}=2 \\ \sqrt[]{12}=2*\sqrt[]{3} \\ \sqrt[]{12}=2\sqrt[]{3} \end{gathered}

Hence, the simplified radical of the example used is


\sqrt[]{12}=2\sqrt[]{3}

User Fernando Cervantes
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