How to find a ratio of square roots - ACT Math
Card 0 of 3
x4 = 100
If x is placed on a number line, what two integers is it between?
x4 = 100
If x is placed on a number line, what two integers is it between?
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.
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.
Compare your answer with the correct one above
and 
What is the ratio of 
to 
?
What is the ratio of
To find a ratio like this, you need to divide 
by 
. Recall that when you have the square root of a fraction, you can "distribute" the square root to the numerator and the denominator. This lets you rewrite 
as:
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:
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:
Compare your answer with the correct one above
What is the ratio of 
to 
?
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
to 
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 
in 
, you can rewrite the numerator:
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 
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
Compare your answer with the correct one above