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Example Question #31 : Arithmetic
Solve for :
To begin solving this problem, find the greatest perfect square for all quantities under a radical. might seem intimidating, but remember that raising even single-digit numbers to the fourth power creates huge numbers. In this case,
is divisible by
, a perfect fourth power.
--->
Pull the perfect terms out of each term on the left:
--->
Next, factor out from the left-hand side:
--->
Lastly, isolate , remembering to simplify the fraction where possible:
--->
Example Question #31 : Arithmetic
Simplify:
To start, begin pulling the largest perfect square you can out of each number:
So, . You can just add the two terms together once they have a common radical.
Example Question #31 : Arithmetic
Simplify:
Again here, it is easiest to recognize that both of our terms are divisible by , a prime number likely to appear in our final answer:
Now, simplify our perfect squares:
Lastly, subtract our terms with a common radical:
Example Question #31 : Arithmetic
Solve for :
To begin solving this problem, find the greatest common perfect square for all quantities under a radical.
--->
Factor out the square root of each perfect square:
--->
Next, factor out from each term on the left-hand side of the equation:
--->
Lastly, isolate :
--->
Example Question #1 : Square Roots And Operations
Find the product:
Simplify the radicals, then multiply:
Example Question #2 : Square Roots And Operations
Simplify the following completely:
To simplify this expression, simply multiply the radicands and reduce to simplest form.
Example Question #1 : How To Multiply Square Roots
Simplify:
When multiplying square roots, the easiest thing to do is first to factor each root. Thus:
Now, when you combine the multiplied roots, it will be easier to come to your final solution. Just multiply together everything "under" the roots:
Finally this can be simplified as:
Example Question #4 : Square Roots And Operations
Simplify the following:
When multiplying square roots, the easiest thing to do is first to factor each root. Thus:
Now, when you combine the multiplied roots, it will be easier to come to your final solution. Remember that multiplying roots is very easy! Just multiply together everything "under" the roots:
Finally this can be simplified as:
Example Question #5 : Square Roots And Operations
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.
Example Question #6 : Square Roots And Operations
Find 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 your radical.
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