ACT Math › Square Roots and Operations
Simplify the following expression:
Begin by factoring out each of the radicals:
For the first two radicals, you can factor out a or
:
The other root values cannot be simply broken down. Now, combine the factors with :
This is your simplest form.
Simplify the following expression:
Begin by factoring out each of the radicals:
For the first two radicals, you can factor out a or
:
The other root values cannot be simply broken down. Now, combine the factors with :
This is your simplest form.
Simplify: .
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 , so too does
.
Simplify: .
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 , so too does
.
Simplify the following:
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 , so too does
.
Simplify the following:
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 , so too does
.
State the product:
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:
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:
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 , so too does
.
Simplify the following:
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 , so too does
.