Adding or subtracting radicals can only be performed when the radicans (the value inside the radical) are the same with the result being adding or subtracting the coefficients. For example
7√ 5 - 3√ 5 = 4√ 5 .
To multiply two radicals combine the coefficients and radicands separately and make sure to try and simplify the combined radical. For example
7√ 6 * 3√ 3 = 21√ 18
= 21√ 9*2 = 63√ 2 .
Remember that a radical expression is only considering simplified if there is no radical in the denominator. To achieve this when dividing, multiply the numerator and denominator of the fraction
by the "conjugate" of the denominator. We know that (a - b)(a + b) = a
2 - b
2, we can use this fact to remove radicals. The conjugate of
(x + √
5 ) would be (x - √
5 ), since
(x + √
5 )(x - √
5 ) = x
2 - 5. So, to simplify
| 1 | = | 1 * (x - √ 5 ) | = | x - √ 5 |
| x + √ 5 | (x + √ 5 )(x - √ 5 ) | x2 - 5 |