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

7\( \sqrt{8} \) x 3\( \sqrt{8} \)
(7 x 3)\( \sqrt{8 \times 8} \)
21\( \sqrt{64} \)

Now we need to simplify the radical:

21\( \sqrt{64} \)
21\( \sqrt{8^2} \)
(21)(8)
168

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

7,815,000 in scientific notation is 7.815 x 10⁶

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

7\( \sqrt{8} \) - 6\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) - 6\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) - 6\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) - 6\( \sqrt{2} \)
14\( \sqrt{2} \) - 6\( \sqrt{2} \)

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

The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 have in common.

To simplify a radical, factor out the perfect squares:

\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)