Example

Find the exact value of 8 times the square root of 3, all over the quantity 5 times the square root of 12 end quantity..

Rationalize the denominator by multiplying the entire expression by the square root of 12 over the square root of 12..
 
 
 
 
The quantity 8 times the square root of 3 end quantity over the quantity 5 times the square root of 12 end quantity • the quantity the square root of 12 over the square root of 12
=
8 times the square root of the quantity 3 times 12 end quantity, divided by the quantity 5 times the square root of the quantity 12 times 12 end quantity, end quantity.

Simplify.
8 times the square root of the quantity 3 times 12 end quantity, divided by the quantity 5 times the square root of the quantity 12 times 12 end quantity, end quantity
=
8 times the square root of 36 over the quantity 5 times the square root of 144 end quantity.


Calculate the perfect squares.
8 times the square root of 36 over the quantity 5 times the square root of 144 end quantity
=
8 times 6, all over the quantity 5 times 12 end quantity = 48 over 60.


Simplify as needed.
48 divided by 12, all over the quantity 60 divided by 12 end quantity
=
4 over 5.


8 times the square root of 3 over the quantity 5 times the square root of 12 end quantity
=
4 over 5.

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