All ACT Math Resources
Example Questions
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.
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Pull the perfect terms out of each term on the left:
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Next, factor out from the left-hand side:
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Lastly, isolate , remembering to simplify the fraction where possible:
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Example Question #11 : Basic Squaring / Square Roots
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 #11 : Basic Squaring / Square Roots
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 #11 : Basic Squaring / Square Roots
Solve for :
To begin solving this problem, find the greatest common perfect square for all quantities under a radical.
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Factor out the square root of each perfect square:
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Next, factor out from each term on the left-hand side of the equation:
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Lastly, isolate :
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