Simplify the following radical expression.

a.)
b.)
c)
c)

Ask by Gardner Collins. in the United States

Jan 26,2025

Question

Simplify the following radical expression. $$ \sqrt{230} $$ a.) $$ 2 \sqrt{740} $$ b.) $$ 4 \sqrt{140} $$ c) $$ 4 \sqrt{70} $$ c) $$ 2 \sqrt{70} $$

UpStudy AI · Accepted Answer

Let's simplify the radical expression $$ \sqrt{230} $$.

**Step 1: Prime Factorization**
First, factorize 230 into its prime factors:
$$
230 = 2 \times 5 \times 23
$$
None of these factors are perfect squares, which means the radical cannot be simplified further.

**Conclusion**
The expression $$ \sqrt{230} $$ is already in its simplest form and cannot be simplified further using integer factors.

However, based on the provided options, it seems there might be a typo in the problem. If the original expression was intended to be $$ \sqrt{280} $$, then the simplification would be:

$$
\sqrt{280} = \sqrt{4 \times 70} = 2\sqrt{70}
$$

In this case, the correct option would be:

**d.) $$ 2 \sqrt{70} $$**

But strictly speaking, for $$ \sqrt{230} $$, none of the provided options are correct.

**Answer:**  
Cannot simplify √230; the expression is already in its simplest form.
Cannot simplify √230; the expression is already in its simplest form.

Simplify the following radical expression.

a.)
b.)
c)
c)

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