Express in simplest radical form.

square root of, 98, end square root, plus, 4, square root of, 2, end square root

98​+42​

To simplify the expression \(\sqrt{98} + 4\sqrt{2}\), let's start by simplifying \(\sqrt{98}\).

### Simplifying \(\sqrt{98}\):

First, factor 98 into its prime factors:

\[
98 = 2 \times 7 \times 7 = 2 \times 7^2
\]

Now, we can express the square root of 98 as:

\[
\sqrt{98} = \sqrt{2 \times 7^2} = \sqrt{7^2 \times 2} = 7\sqrt{2}
\]

So, \(\sqrt{98}\) simplifies to \(7\sqrt{2}\).

### Simplifying the entire expression:

Now, substitute \(7\sqrt{2}\) for \(\sqrt{98}\) in the original expression:

\[
\sqrt{98} + 4\sqrt{2} = 7\sqrt{2} + 4\sqrt{2}
\]

Since both terms have the same radical \(\sqrt{2}\), we can combine them:

\[
7\sqrt{2} + 4\sqrt{2} = (7 + 4)\sqrt{2} = 11\sqrt{2}
\]

Thus, the simplest radical form of the expression is:

\[
\boxed{11\sqrt{2}}
\]

Would you like more details or have any questions? Here are some related questions:

1. Simplify \(\sqrt{72} + 2\sqrt{2}\).
2. What is the simplest radical form of \(\sqrt{50} + 5\sqrt{2}\)?
3. How do you simplify \(2\sqrt{18} + 3\sqrt{2}\)?
4. What is the result of \(3\sqrt{8} + \sqrt{2}\) in simplest radical form?
5. Simplify \(\sqrt{128} + 6\sqrt{2}\).

**Tip:** When adding or subtracting radicals, combine only like terms, meaning they must have the same radicand.

Learn how to simplify the expression sqrt(98) + 4sqrt(2) step-by-step. Understand the process of simplifying radicals and combining like terms. Suitable for high school students studying algebra and advanced mathematics.

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