To subtract these radicals together their radicands must be the same:

2\( \sqrt{8} \) - 8\( \sqrt{2} \)
2\( \sqrt{4 \times 2} \) - 8\( \sqrt{2} \)
2\( \sqrt{2^2 \times 2} \) - 8\( \sqrt{2} \)
(2)(2)\( \sqrt{2} \) - 8\( \sqrt{2} \)
4\( \sqrt{2} \) - 8\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{5} \) x 6\( \sqrt{3} \)
(7 x 6)\( \sqrt{5 \times 3} \)
42\( \sqrt{15} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{4}} \)
\( \frac{\sqrt{49}}{\sqrt{4}} \)
\( \frac{\sqrt{7^2}}{\sqrt{2^2}} \)
\( \frac{7}{2} \)
3\(\frac{1}{2}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{24\sqrt{4}}{8\sqrt{2}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{4}{2}} \)
3 \( \sqrt{2} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)