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

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

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

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

3\( \sqrt{7} \) x 8\( \sqrt{7} \)
(3 x 8)\( \sqrt{7 \times 7} \)
24\( \sqrt{49} \)

Now we need to simplify the radical:

24\( \sqrt{49} \)
24\( \sqrt{7^2} \)
(24)(7)
168

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.