UNIT 1 — MILESTONE 1
18/19
18/19 that's 95% RETAKE
18 questions were answered correctly.
1 question was answered incorrectly.
1
Write the following expression as a single integer.
-(-15) – 45
60
30
-30
-60
RATIONALE
To solve this problem, we can use Order of
Operations. First consider the sign of the first number.
There is a negative number outside the parentheses,
which means we must take the opposite of the number
inside the parentheses.
The opposite of negative 15 is positive 15, so -
(-15) evaluates to 15. Next, subtract 45 from 15.
, 15 minus 45 equals -30.
UNIT 1 — MILESTONE 1
CONCEPT
Adding and Subtracting Positive and Negative Numbers 18/19
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2
Simplify the following radical expression.
RATIONALE
To simplify this expression, we can use the Product
Property of Radicals to separate the expression into two
radicals.
The cube root of can be written as the cube root
of 64 times the cube root of . Next, we can write each
radical expression using a fractional exponent in order
to simplify. The index of the radical determines the
denominator of the fractional exponent. The index here
, is 3, so each expression underneath the radical will be
UNIT 1 — MILESTONE
raised to the power.
1
Now that we have changed our original expression 18/19
from a radical to fractional exponents, we can evaluate
and simplify the two expressions that are raised to the
power.
to the power of evaluates to 4 because 4 raised
to the 3rd power is 64 ( ). To simplify , we
multiply the two exponents together.
3 times equals 1 and is simply x. The expression
simplifies to 4x.
CONCEPT
Applying the Properties of Radicals
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3
Jayla bought the ingredients to make chicken soup, and wanted
to make a double batch, which would be 12 cups of soup. A quick
Google search told her that this was 173.3 cubic inches. She
hoped the soup pot below would be big enough.
18/19
18/19 that's 95% RETAKE
18 questions were answered correctly.
1 question was answered incorrectly.
1
Write the following expression as a single integer.
-(-15) – 45
60
30
-30
-60
RATIONALE
To solve this problem, we can use Order of
Operations. First consider the sign of the first number.
There is a negative number outside the parentheses,
which means we must take the opposite of the number
inside the parentheses.
The opposite of negative 15 is positive 15, so -
(-15) evaluates to 15. Next, subtract 45 from 15.
, 15 minus 45 equals -30.
UNIT 1 — MILESTONE 1
CONCEPT
Adding and Subtracting Positive and Negative Numbers 18/19
Report an issue with this question
2
Simplify the following radical expression.
RATIONALE
To simplify this expression, we can use the Product
Property of Radicals to separate the expression into two
radicals.
The cube root of can be written as the cube root
of 64 times the cube root of . Next, we can write each
radical expression using a fractional exponent in order
to simplify. The index of the radical determines the
denominator of the fractional exponent. The index here
, is 3, so each expression underneath the radical will be
UNIT 1 — MILESTONE
raised to the power.
1
Now that we have changed our original expression 18/19
from a radical to fractional exponents, we can evaluate
and simplify the two expressions that are raised to the
power.
to the power of evaluates to 4 because 4 raised
to the 3rd power is 64 ( ). To simplify , we
multiply the two exponents together.
3 times equals 1 and is simply x. The expression
simplifies to 4x.
CONCEPT
Applying the Properties of Radicals
Report an issue with this question
3
Jayla bought the ingredients to make chicken soup, and wanted
to make a double batch, which would be 12 cups of soup. A quick
Google search told her that this was 173.3 cubic inches. She
hoped the soup pot below would be big enough.
