To multiply radicals, consider the following, √(25) * √(9) = 5 * 3 = 15 and √(25) * √(9) = √(225) = 15, so √(25) * √(9) = √(25*9).
as a general rule, √(a) * √(b) = √(ab)
To simplify radicals, such as √(72), where there is no perfect square, you need to take the square out, so it would be √(2*6²), which would simplify as 6√2
To divide radicals, consider the following, √(25)/√(9) = 5/3 and √(25)/√(9) = √(25/9) = √(5/3)² = 5/3
as a general rule, if a and b are real numbers, and b does not equal zero, √(a)/√(b) = √(a/b)
To rationalize the denominator, such as √(5)/√(3), make the bottom a perfect square, like this, √(5*3)/√(3*3). I multiplied both the top and bottom by √(3)/√(3) to make the denominator a perfect square, making the problem look like √(15)/3, which is rationalized.
*note, a number with an exponent of 1/2 is equal to taking the square root of it, an exponent of 1/3 is the same as the cube root.*
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