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3 votes
How to make (11/3)^(3/2) become square root 33 ?

User Wild Beard
by
3.6k points

1 Answer

7 votes

Answer:

11sqrt(33)

------------

9

Explanation:

(11/3)^(3/2)

Apply the cube to inside:

(11^3/3^3)^(1/2)

Recall (x^3)^(1/2)=sqrt(x^3)=sqrt(x^2)×sqrt(x)=x×sqrt(x)

So we have:

11sqrt(11)

------------

3sqrt(3)

Rationalize denominator by multiplying top and bottom by sqrt(3):

11sqrt(11)sqrt(3)

------------

3sqrt(3)sqrt(3)

=

11sqrt(33)

------------

3(3)

=

11sqrt(33)

------------

9

User Swapnil Kale
by
4.1k points