dividing radical expressions
√5k^4 + 3√2k
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√3k^3
To divide radical expressions, you can use the rationalizing method. The rationalizing method helps eliminate the radical in the denominator by multiplying both the numerator and the denominator by a conjugate, which is the expression with the opposite sign between the radical terms.
Let's divide the given radical expressions:
√(5k^4) + 3√(2k)
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√(3k^3)
First, let's rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator (which is √(3k^3)).
(√(5k^4) + 3√(2k))(√(3k^3))/(√(3k^3))
Now, we can simplify the expression by multiplying across the numerator and denominator:
(√(5k^4) * √(3k^3) + 3√(2k) * √(3k^3)) / (√(3k^3) * √(3k^3))
Simplify the multiplication of the radicals:
√(15k^7) + 3√(6k^4) / √(9k^6)
Since the denominator has a radical, let's simplify further:
√(15k^7) + 3√(6k^4) / 3k^3
To simplify this division further, we can divide each term in the numerator and denominator by 3k^3:
(√(15k^7) + 3√(6k^4)) / 3k^3
And that's the simplified expression for the division of the given radical expressions.