Express in simplest radical form.

square root of, 162, end square root

162

To simplify the square root of 162, we can factor it into its prime factors and look for any perfect square factors.

First, let's factor 162:

\[
162 = 2 \times 81
\]
\[
81 = 9 \times 9 = 3 \times 3 \times 3 \times 3
\]

So, the prime factorization of 162 is:

\[
162 = 2 \times 3 \times 3 \times 3 \times 3 = 2 \times 3^4
\]

Now, we can simplify \(\sqrt{162}\):

\[
\sqrt{162} = \sqrt{2 \times 3^4}
\]

Recognizing that \(3^4\) is a perfect square \((3^2)^2\), we can simplify further:

\[
\sqrt{162} = \sqrt{2 \times (3^2) \times (3^2)} = 3 \times 3 \times \sqrt{2} = 9\sqrt{2}
\]

So, the square root of 162 in simplest radical form is \(9\sqrt{2}\).

Would you like to explore more examples or have any questions?

Here are 5 related questions for further practice:
1. Simplify \(\sqrt{72}\) into simplest radical form.
2. What is the square root of 50 in simplest radical form?
3. Express \(\sqrt{200}\) in simplest radical form.
4. Simplify \(\sqrt{98}\) into simplest radical form.
5. How do you simplify the square root of a non-perfect square?

**Tip:** When simplifying square roots, always look for the largest perfect square factor to extract the simplest form.

Discover how to simplify the square root of 162 into simplest radical form. Follow our detailed step-by-step guide with prime factorization and square root simplification. Suitable for students in Grades 9-12.

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