Square Roots and Operations
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ACT Math › Square Roots and Operations
Simplify the following expression:
Explanation
Begin by factoring out each of the radicals:
For the first two radicals, you can factor out a 
The other root values cannot be simply broken down. Now, combine the factors with 
This is your simplest form.
Simplify the following expression:
Explanation
Begin by factoring out each of the radicals:
For the first two radicals, you can factor out a
The other root values cannot be simply broken down. Now, combine the factors with
This is your simplest form.
Simplify: 
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as 
Simplify:
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as
Simplify the following:
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as 
Simplify the following:
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as
State the product:
Explanation
Don't try to do too much at first for this problem. Multiply your radicals and your coefficients, then worry about any additional simplification.
Now simplify the radical.
State the product:
Explanation
Don't try to do too much at first for this problem. Multiply your radicals and your coefficients, then worry about any additional simplification.
Now simplify the radical.
Simplify the following:
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as 
Simplify the following:
Explanation
Begin simplifying by breaking apart the square roots in question. Thus, you know:
Now, with square roots, you can combine factors just as if a given root were a variable. So, just as