Sophia Practice Milestone 1 Radical Expressions & Unit 1
Conversions Questions And Answers
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RETAKE THIS PRACTICE MILESTONE
1 ●
RATIONALE
To simplify this expression, we can use the Product Property of Radicals to separate the expression into two
radicals.
The fourth root of can be written as the fourth root of 81 times the fourth root of .
Next, we can write each radical expression using a fractional exponent in order to
simply. The index of the radical determines the denominator of the fractional exponent. The index here is 4, so
each expression underneath the radical will be raised to the power.
Now that we have changed our original expression from a radical to fractional exponents, we can evaluate and
simplify the two expressions that are raised to the power.
81 to the power of evaluates to 3 because 3 raised to the 4th power is 81 (
). To simplify , we multiply the two exponents together.
4 times equals 1 and is simply x. The expression simplifies to 3x.
CONCEPT
→ Applying the Properties of Radicals Report an issue with this question
, 2●
Trevor spent 3.25 hours cleaning his house.
How many seconds is 3.25 hours?
902 seconds
●
11,700 seconds
195 seconds
●
● 54,166 seconds
RATIONALE
In general, we use conversion factors to convert from one unit to another.
A conversion factor is a fraction with equal quantities in the numerator
and denominator, but written with different units.
We want to convert hours to seconds. We might not know off-hand how
many seconds are in an hour, but we know how many seconds are in a
minute, and how many minutes are in an hour. We will use these facts to
set up conversion factors.
There are 60 minutes in 1 hour and 60 seconds in 1 minute. To
by
the
fractions
Notice how the fractions are set up. The units of hours and minutes will
cancel, leaving only seconds. Finally we can evaluate the multiplication by
multiplying across the numerator and denominator.
In the numerator, 3.25 times 60 times 60 equals 11700. The last step is to
simplify the fraction.
3.25 hours is equivalent to 11700 seconds.
CONCEPT
→ Converting Units
Report an issue with this question
Conversions Questions And Answers
,19/19 that's 100%
RETAKE THIS PRACTICE MILESTONE
1 ●
RATIONALE
To simplify this expression, we can use the Product Property of Radicals to separate the expression into two
radicals.
The fourth root of can be written as the fourth root of 81 times the fourth root of .
Next, we can write each radical expression using a fractional exponent in order to
simply. The index of the radical determines the denominator of the fractional exponent. The index here is 4, so
each expression underneath the radical will be raised to the power.
Now that we have changed our original expression from a radical to fractional exponents, we can evaluate and
simplify the two expressions that are raised to the power.
81 to the power of evaluates to 3 because 3 raised to the 4th power is 81 (
). To simplify , we multiply the two exponents together.
4 times equals 1 and is simply x. The expression simplifies to 3x.
CONCEPT
→ Applying the Properties of Radicals Report an issue with this question
, 2●
Trevor spent 3.25 hours cleaning his house.
How many seconds is 3.25 hours?
902 seconds
●
11,700 seconds
195 seconds
●
● 54,166 seconds
RATIONALE
In general, we use conversion factors to convert from one unit to another.
A conversion factor is a fraction with equal quantities in the numerator
and denominator, but written with different units.
We want to convert hours to seconds. We might not know off-hand how
many seconds are in an hour, but we know how many seconds are in a
minute, and how many minutes are in an hour. We will use these facts to
set up conversion factors.
There are 60 minutes in 1 hour and 60 seconds in 1 minute. To
by
the
fractions
Notice how the fractions are set up. The units of hours and minutes will
cancel, leaving only seconds. Finally we can evaluate the multiplication by
multiplying across the numerator and denominator.
In the numerator, 3.25 times 60 times 60 equals 11700. The last step is to
simplify the fraction.
3.25 hours is equivalent to 11700 seconds.
CONCEPT
→ Converting Units
Report an issue with this question
