Radicals and radicals equations step through examples, closing questions and more info etc. 

追加: 2026-06-06

[00:00:01]To simplify radicals, I look for perfect squares inside the radical because the square root of a perfect square can be taken out of the radical.

[00:00:10]This works because the square root of a product equals a product of the square roots. For example, if Johnny has radical 36 bars of soap, then radical 36 equals 6. So, Johnny has six bars of soap. If Johnny has radical 72 bars of soap, then radical 72 equals radical in in parentheses 36 multiplied by two equal radical 36 * 2 equals 6 to the radical of 2.

[00:00:49]So, Johnny has 6 to the radical of 2 bars of soap.

[00:00:52]Radicals can also be combined when they have the same number inside the radical.

[00:00:59]For example, if Johnny has 2 to the radical 3 bars of soap and buys 4 to the radical 3 more, then 2 to the radical 3 3 + 4 to the radical 3 equals 6 to the radical of 3.

[00:01:16]However, [snorts] radicals cannot be combined if the numbers inside are different. For example, 3 to the radical of 2 + 2 to the radical of 5 cannot be simplified because radical 2 and radical 5 are different radicals.

[00:01:34]When solving radical equations, it is different and important to check for extraneous solutions.

[00:01:45]For example, radical in parentheses x + 1 equals 2.

[00:01:51]Squaring both sides gives x + 1 = 4, so x = 3. Checking the answer gives radical parentheses 3 + 1 = radical 4 = 2, so x = 3 works. Another example is radical x = x - -2. Squaring both sides gives x = to the power of 2 = x to the power of 2 -4x + 4. Moving everything to one side gives 0 = x to the power of 2 -5 x + 4, which factors to 0 = ( x - 1) ( x - 1) (x -