Question

Simplify the expression. Write your answer in simplest radical form.(1 point)
210−−√−40−−√=

Answer 1

To simplify the expression \( \sqrt{210} - \sqrt{40} \), we first need to simplify \( \sqrt{40} \).

We can factor \( 40 \) as follows:
\[
40 = 4 \times 10
\]
Thus,
\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
\]

Now we substitute this back into the expression:
\[
\sqrt{210} - \sqrt{40} = \sqrt{210} - 2\sqrt{10}
\]

At this point, we check if \( \sqrt{210} \) can be simplified. The prime factorization of \( 210 \) is:
\[
210 = 2 \times 3 \times 5 \times 7
\]
Since there are no pairs of prime factors, \( \sqrt{210} \) cannot be simplified further.

Thus, the expression remains:
\[
\sqrt{210} - 2\sqrt{10}
\]

So, the simplified form of \( \sqrt{210} - \sqrt{40} \) is:
\[
\sqrt{210} - 2\sqrt{10}
\]