ACT Math : How to find a ratio of square roots
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Example Questions
Example Question #1 : Square Roots And Operations
x4 = 100
If x is placed on a number line, what two integers is it between?
4 and 5
5 and 6
3 and 4
Cannot be determined
2 and 3
3 and 4
It might be a little difficult taking a fourth root of 100 to isolate x by itself; it might be easier to select an integer and take that number to the fourth power. For example 34 = 81 and 44 = 256. Since 34 is less than 100 and 44 is greater than 100, x would lie between 3 and 4.
Example Question #1 : How To Find A Ratio Of Square Roots
What is the ratio of 
The ratio of two numbers is merely the division of the two values. Therefore, for the information given, we know that the ratio of
can be rewritten:
Now, we know that the square root in the denominator can be "distributed" to the numerator and denominator of that fraction:
Thus, we have:
To divide fractions, you multiply by the reciprocal:
Now, since there is one 
This gives you:
Rationalize the denominator by multiplying both numerator and denominator by 
Let's be careful how we write the numerator so as to make explicit the shared factors:
Now, reduce:
This is the same as
Example Question #1 : How To Find A Ratio Of Square Roots
What is the ratio of 
To find a ratio like this, you need to divide 
Next, you can write the ratio of the two variables as:
Now, when you divide by a fraction, you can rewrite it as the multiplication by the reciprocal. This gives you:
Simplifying, you get:
You should rationalize the denominator:
This is the same as:
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