a) The square root of is , because .

b) of is , because .

c) The average of and is , because .

Therefore (b) and (c) are equal, and they are both smaller than (a).

a) The square root of is , because .

b) of is , because .

c) The average of and is , because .

Therefore (b) and (c) are equal, and they are both smaller than (a).

To find a percentage of the number, multiply it by the decimal version of the percent, or the percent divided by .

Therefore, percent of is equal to , or

To find a percentage of the number, multiply it by the decimal version of the percent, or the percent divided by .

Therefore, percent of is equal to , or

Multiply the fractions by the integers in order to compare the expressions:

a)

b)

c)

It is now clear that (b) is smaller than (a), which is smaller than (c).

Multiply the fractions by the integers in order to compare the expressions:

a)

b)

c)

It is now clear that (b) is smaller than (a), which is smaller than (c).

You don't need to calculate any square roots to solve this problem! Just remember the following property:

Following this property, (a) and (b) are equal:

This also means that the following is true:

And therefore:

(c) is just a simplified version of (a) and (b)

You don't need to calculate any square roots to solve this problem! Just remember the following property:

Following this property, (a) and (b) are equal:

This also means that the following is true:

And therefore:

(c) is just a simplified version of (a) and (b)

Calculate each expression in order to compare them:

a) of

b) of

c) of

(b) and (c) are equal, and (a) is greater than both.

a)

This expression is already simplified.

b)

This expression simplifies to .

c)

This expression also simplifies to .

Clearly (b) and (c) are equal, but (a) is smaller because it has a smaller numerator.