Respuesta :
Answer:
B is the answer
Step-by-step explanation:
Given :[tex]\sqrt[3]{5} \times \sqrt{2}[/tex]
A)[tex]\sqrt[6]{10}[/tex]
[tex]\sqrt[6]{5 \times 2}[/tex]
[tex]5^{\frac{1}{6}} \times 2^{\frac{1}{6}}[/tex]
[tex]5^{\frac{1}{3}\times \frac{1}{2}} \times 2^{\frac{1}{3}\times \frac{1}{2}}[/tex]
[tex]5^{(\frac{1}{3})\frac{1}{2}} \times 2^{(\frac{1}{3}) \frac{1}{2}}[/tex]
[tex]\sqrt[3]{5^{\frac{1}{2}}} \times \sqrt{2^{\frac{1}{3}}}[/tex]
B)[tex]\sqrt[6]{200}[/tex]
[tex]\sqrt[6]{5 \times 5 \times 8}[/tex]
[tex]\sqrt[6]{5^2 \times 2^3}[/tex]
[tex]5^{\frac{2}{6}} \times 2^{\frac{3}{6}}[/tex]
[tex]5^{\frac{1}{3}} \times 2^{\frac{1}{2}}[/tex]
[tex]\sqrt[3]{5} \times \sqrt{2}[/tex]
C)[tex]\sqrt[6]{200}[/tex]
[tex]\sqrt[6]{5 \times 5 \times 5 \times 2 \times 2}[/tex]
[tex]\sqrt[6]{5^3 \times 2^2}[/tex]
[tex]5^{\frac{3}{6}} \times 2^{\frac{2}{6}}[/tex]
[tex]5^{\frac{1}{2}} \times 2^{\frac{1}{3}}[/tex]
[tex]\sqrt{5} \times \sqrt[3]{2}[/tex]
D)[tex]\sqrt[6]{100000}[/tex]
[tex]\sqrt[6]{5^5 \times 2^5}[/tex]
[tex]5^{\frac{5}{6}} \times 2^{\frac{5}{6}}[/tex]
[tex]\sqrt[6]{5^5} \times \sqrt[6]{2^5}[/tex]
So, B is the answer
The surd [tex]\sqrt[3]{5} * \sqrt{2}[/tex] is equal to the radical [tex]\sqrt[6]{200}[/tex] which makes option B the answer.
Data;
- [tex]\sqrt[3]{5} * \sqrt{2}[/tex]
we are given a series of surds values to compare which is equal to the one above.
To solve this, we must perform some operations with the basic rules of surds or radicals.
Taking option A and solving to compare the value with our expected answer,
[tex]\sqrt[6]{10} = 5^\frac{1}{6} * 2^\frac{1}{6}=5^\frac{1}{3}^*^\frac{1}{2} * 2^\frac{1}{3}^*^\frac{1}{2}\\ \sqrt[3]{5^\frac{1}{2} } * \sqrt{2^\frac{1}{3} }[/tex]
This is incorrect as it is not equal to the expected value
Let's take option B
[tex]\sqrt[6]{200}=\sqrt[6]{5*5*8}=\sqrt[6]{5^2*2^3}=5^\frac{1}{3} * 2^\frac{1}{2}=\\=\sqrt[3]{5} * \sqrt{2}[/tex]
This answer is correct as this gives the expected value to this question.
We can check further options but since we are expecting one of the options to be the answer, we can eliminate other options since we already have our answer.
The answer to this question is option B
Learn more on radicals here;
https://brainly.com/question/9483387
https://brainly.com/question/1603441
