Web a radical equation is any equation that contains one or more radicals with a variable in the radicand. Solve x = 8 solution: Steps 1 and eliminat 2 if necessary. Consider the example and try to come up with the solution. Factoring, combining like terms,…) to isolate the variable. Raise both sides of the equation to the “nth” power. √2x − 1 = 3. 1) x = 10 {100} 2) 10 = m 10 {1000} 3) v − 4 = 3 {13} 4) 6 = v − 2 {38} 5) n = 9 {81} 6) 5 = x + 3 {22} 7) 2 = 4b {1} 8) n + 9 = 1 {−8} 9) −8 + 5a − 5 = −3 {6} 10) 10 9x = 60 {4} 11) 1 = x − 5 {6} 12) −10 v − 10 = −60 Remember to check for extraneous solutions. Following are some examples of radical equations, all of which will be solved in this section:
Solve x = 8 solution: √2x − 1 = 3. Solve an equation with a single square root using the squaring property of equality. 3√4x2 + 7 − 2 = 0. Web worksheet how to solve equations with radical expressions checking your answer on is required because solutions may be extraneous. =8 ( x 2(8)2 =64 64=8 8=8 1) x = 10 {100} 2) 10 = m 10 {1000} 3) v − 4 = 3 {13} 4) 6 = v − 2 {38} 5) n = 9 {81} 6) 5 = x + 3 {22} 7) 2 = 4b {1} 8) n + 9 = 1 {−8} 9) −8 + 5a − 5 = −3 {6} 10) 10 9x = 60 {4} 11) 1 = x − 5 {6} 12) −10 v − 10 = −60 Consider the example and try to come up with the solution. Isolate the radical(s) and identify the index (n). 1) 110 − n = n {10} 2) p = 2 − p {1} 3) 30 − x = x {5} 4) x = 8x {0, 8} 5) x = 42 − x {6} 6) 12 − r = r {3} 7) 4n = n {0, 4} 8) 5v = v {0, 5} 9) r = 10 r {0, 10} 10) m = 56 − m {7} 11) b = −4 + 4b {2} 12) r = 8r {0, 8} Steps 1 and eliminat 2 if necessary.
