Challenge!
Rationalize the denominator of [tex]\dfrac{1}{\sqrt[3]{4} +\sqrt[3]{6} +\sqrt[3]{9} }[/tex].
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We have to rationalise the denominator of the following fraction -
So, this fraction can be written a,
Cube root of a number is the number raised to the power 1/3.
Now, let us assume that,
Then the fraction becomes,
Rationalizing factor = (x - y). Multiply both numerator and denominator by (x - y). We get,
Putting the values, we get,
Which is our required answer.
Calculate the square root of 4 and get 2.
Multiply 3 and 2 to get 6.
Calculate the square root of 9 and get 3.
Rationalize the denominator
by multiplying numerator and denominator by
Consider
Multiplication can be transformed into difference of squares using the rule: