1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lena [83]
3 years ago
15

What expression is equivalent to ^3 square root of 2y^3 times 7 square root of 18y

Mathematics
1 answer:
Mumz [18]3 years ago
6 0

Answer:

\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})

Step-by-step explanation:

The question is poorly formatted.

Given

\sqrt[3]{2y^3} * 7\sqrt{18y}

Required

Derive an equivalent expression

\sqrt[3]{2y^3} * 7\sqrt{18y}

Express 18 as 9 * 2

\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}

Split the expression as follows:

\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}

Take positive square root of 9

\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}

\sqrt[3]{2y^3} * 21 * \sqrt{2y}

21*\sqrt[3]{2y^3} *  \sqrt{2y}

The cube root can be rewritten to give:

21*\sqrt[3]{2}*\sqrt[3]{y^3} *  \sqrt{2y}

\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y

So, we have:

21*\sqrt[3]{2} * y *  \sqrt{2y}

Rewrite as:

21y *\sqrt[3]{2}  *  \sqrt{2y}

Split \sqrt{2y

21y *\sqrt[3]{2}  *  \sqrt{2} * \sqrt{y}

Collect Like Terms

21y*\sqrt{y} *\sqrt[3]{2}  *  \sqrt{2}

Represent in index form

21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}

Apply law of indices

21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }

21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}

21*y^{\frac{3}{2}} *2^{\frac{5}{6}}

21(y^{\frac{3}{2}})(2^{\frac{5}{6}})

Hence:

\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})

You might be interested in
2(x+3) + 6 = 3x - 9 written in word form? HELP!!!
zheka24 [161]
Two multiplied by x plus three plus six is equal to three multiplied by x subtracted by nine
7 0
3 years ago
Evaluate the expression if x=2 and y=1 -4+|y-6|
belka [17]
The answer is one because according to pemdas you must do the parentheses first then do the rest
5 0
3 years ago
3/5 1/2 3/4 8/10 from least to greatest
NNADVOKAT [17]

Answer: it’s 8/10, 3/5, 3/4, 1/2

Step-by-step explanation:1/2 is greater than the other numbers

3 0
2 years ago
Read 2 more answers
PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!! The line plot shows the results of a survey of 10 boys and 10 girls about how many tim
Alchen [17]

Answer:

I think the answer is D. On average, boys saw the movie more than girls.

Do great on the test! ~ :)

7 0
3 years ago
Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”?
jekas [21]
<span>We know that p is the statement x = 4 and that q is y = -2 . Then we have that the statement "If x = 4 then y = -2" can be written as "if p then q" . Then we can represent "If p then q" as p ---> .</span>
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the measure of arc AC? <br>m&lt; ABC = 78 degrees<br> A.156<br> B.78<br> C.39<br> D.13
    11·1 answer
  • A man is walking across a 300 foot long field at the same time his daughter is walking towards him from the opposite end. The ma
    15·1 answer
  • PLEASE ASSIST ME WITH THIS
    9·2 answers
  • Approximate value of x and why
    5·2 answers
  • 15) JoJo runs at a rate of 6 miles per hour. How many<br>miles will he run in 3 hours?​
    14·2 answers
  • Determine which number would satisfy the inequality 3y-8&gt;22. Choose all that apply.
    7·1 answer
  • In 1983, a hardcover dictionary cost $145.75. If the CPI is currently 209, what would a hardcover dictionary cost today? Round t
    15·2 answers
  • A submarine is running at a depth of 235 ft underwater. It changes course and rises 101 ft. What is the change in elevation?
    11·1 answer
  • Solve PLS HELPPPPP PLS HELP PLS HELP PLS HELPP
    11·2 answers
  • Help please!<br> Select the correct answer.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!