## Example Questions

### Example Question #1 : How To Find A Ratio Of Square Roots

x= 100

If x is placed on a number line, what two integers is it between?

5 and 6

2 and 3

Cannot be determined

3 and 4

4 and 5

3 and 4

Explanation:

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 3= 81 and 4= 256. Since 34 is less than 100 and 44 is greater than 100, x would lie between 3 and 4.

### Example Question #2 : How To Find A Ratio Of Square Roots

What is the ratio of to ?      Explanation:

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 ### Example Question #3 : How To Find A Ratio Of Square Roots and What is the ratio of to ?      Explanation:

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: ### All ACT Math Resources 