Math / Algebra

QuestionSelect the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ? A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$

Studdy Solution

STEP 1

1. We are given an expression involving cube roots and need to simplify it.
2. The expression involves like terms, which can be combined.
3. The goal is to find the equivalent expression from the given options.

STEP 2

1. Identify and combine like terms in the expression $21 \sqrt[3]{15} - 9 \sqrt[3]{15}$ .
2. Compare the simplified expression to the given options to select the correct answer.

STEP 3

Identify the like terms in the expression. Both terms have the cube root of 15, which means they can be combined:
$21 \sqrt[3]{15} - 9 \sqrt[3]{15}$
Combine the coefficients of the like terms:
$(21 - 9) \sqrt[3]{15}$

STEP 4

Simplify the expression by performing the subtraction:
$12 \sqrt[3]{15}$

STEP 5

Compare the simplified expression $12 \sqrt[3]{15}$ with the given options:
A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$
The correct answer is option D: $12 \sqrt[3]{15}$ .

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QuestionSelect the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ? A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$

Studdy Solution

STEP 1

1. We are given an expression involving cube roots and need to simplify it.
2. The expression involves like terms, which can be combined.
3. The goal is to find the equivalent expression from the given options.

STEP 2

1. Identify and combine like terms in the expression $21 \sqrt[3]{15} - 9 \sqrt[3]{15}$ .
2. Compare the simplified expression to the given options to select the correct answer.

STEP 3

Identify the like terms in the expression. Both terms have the cube root of 15, which means they can be combined:
$21 \sqrt[3]{15} - 9 \sqrt[3]{15}$
Combine the coefficients of the like terms:
$(21 - 9) \sqrt[3]{15}$

STEP 4

Simplify the expression by performing the subtraction:
$12 \sqrt[3]{15}$

STEP 5

Compare the simplified expression $12 \sqrt[3]{15}$ with the given options:
A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$
The correct answer is option D: $12 \sqrt[3]{15}$ .

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QuestionSelect the correct answer.Which expression is equivalent to 21153−915321 \sqrt[3]{15}-9 \sqrt[3]{15}21315​−9315​ ? A. 12 B. 3015330 \sqrt[3]{15}30315​ C. 125312 \sqrt[3]{5}1235​ D. 1215312 \sqrt[3]{15}12315​

Studdy Solution

STEP 1

1. We are given an expression involving cube roots and need to simplify it.2. The expression involves like terms, which can be combined.3. The goal is to find the equivalent expression from the given options.

STEP 2

1. Identify and combine like terms in the expression 21153−9153 21 \sqrt[3]{15} - 9 \sqrt[3]{15} 21315​−9315​.2. Compare the simplified expression to the given options to select the correct answer.

STEP 3

Identify the like terms in the expression. Both terms have the cube root of 15, which means they can be combined:21153−9153 21 \sqrt[3]{15} - 9 \sqrt[3]{15} 21315​−9315​Combine the coefficients of the like terms:(21−9)153 (21 - 9) \sqrt[3]{15} (21−9)315​

STEP 4

Simplify the expression by performing the subtraction:12153 12 \sqrt[3]{15} 12315​

STEP 5

Compare the simplified expression 12153 12 \sqrt[3]{15} 12315​ with the given options:A. 12 B. 30153 30 \sqrt[3]{15} 30315​ C. 1253 12 \sqrt[3]{5} 1235​ D. 12153 12 \sqrt[3]{15} 12315​ The correct answer is option D: 12153 12 \sqrt[3]{15} 12315​.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSelect the correct answer.
Which expression is equivalent to $21 \sqrt[3]{15}-9 \sqrt[3]{15}$ ? A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$

1. We are given an expression involving cube roots and need to simplify it.
2. The expression involves like terms, which can be combined.
3. The goal is to find the equivalent expression from the given options.

1. Identify and combine like terms in the expression $21 \sqrt[3]{15} - 9 \sqrt[3]{15}$ .
2. Compare the simplified expression to the given options to select the correct answer.

Identify the like terms in the expression. Both terms have the cube root of 15, which means they can be combined:
$21 \sqrt[3]{15} - 9 \sqrt[3]{15}$
Combine the coefficients of the like terms:
$(21 - 9) \sqrt[3]{15}$

Simplify the expression by performing the subtraction:
$12 \sqrt[3]{15}$

Compare the simplified expression $12 \sqrt[3]{15}$ with the given options:
A. 12 B. $30 \sqrt[3]{15}$ C. $12 \sqrt[3]{5}$ D. $12 \sqrt[3]{15}$
The correct answer is option D: $12 \sqrt[3]{15}$ .