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

9\( \sqrt{4} \) x 8\( \sqrt{4} \)
(9 x 8)\( \sqrt{4 \times 4} \)
72\( \sqrt{16} \)

Now we need to simplify the radical:

72\( \sqrt{16} \)
72\( \sqrt{4^2} \)
(72)(4)
288

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:

\( \sqrt{\frac{64}{16}} \)
\( \frac{\sqrt{64}}{\sqrt{16}} \)
\( \frac{\sqrt{8^2}}{\sqrt{4^2}} \)
\( \frac{8}{4} \)
2

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

\( \frac{8\sqrt{21}}{4\sqrt{7}} \)
\( \frac{8}{4} \) \( \sqrt{\frac{21}{7}} \)
2 \( \sqrt{3} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)

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

2\( \sqrt{28} \) + 7\( \sqrt{7} \)
2\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
2\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(2)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
4\( \sqrt{7} \) + 7\( \sqrt{7} \)

Now that the radicands are identical, you can add them together: