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

3\( \sqrt{50} \) + 8\( \sqrt{2} \)
3\( \sqrt{25 \times 2} \) + 8\( \sqrt{2} \)
3\( \sqrt{5^2 \times 2} \) + 8\( \sqrt{2} \)
(3)(5)\( \sqrt{2} \) + 8\( \sqrt{2} \)
15\( \sqrt{2} \) + 8\( \sqrt{2} \)

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

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

3\( \sqrt{125} \) - 2\( \sqrt{5} \)
3\( \sqrt{25 \times 5} \) - 2\( \sqrt{5} \)
3\( \sqrt{5^2 \times 5} \) - 2\( \sqrt{5} \)
(3)(5)\( \sqrt{5} \) - 2\( \sqrt{5} \)
15\( \sqrt{5} \) - 2\( \sqrt{5} \)

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

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{17 + 11 + 17 + 11}{4} \) = \( \frac{56}{4} \) = 14

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

5x⁵ + 4x⁵
(5 + 4)x⁵
9x⁵