Experience the convenience of getting your questions answered at IDNLearn.com. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.
Sagot :
To simplify the expression [tex]\(\sqrt{x^2 y^6}\)[/tex], let's go through the following steps:
1. Understand the Expression Inside the Square Root:
The expression inside the square root is [tex]\(x^2 y^6\)[/tex].
2. Break Down the Terms:
We can break down the terms inside the square root based on their properties:
[tex]\[\sqrt{x^2 y^6} = \sqrt{x^2 \cdot y^6}\][/tex]
3. Apply the Square Root to Each Part:
The square root of a product is the product of the square roots:
[tex]\[\sqrt{x^2 \cdot y^6} = \sqrt{x^2} \cdot \sqrt{y^6}\][/tex]
4. Simplify Each Square Root Separately:
- For [tex]\(\sqrt{x^2}\)[/tex]:
[tex]\[\sqrt{x^2} = |x|\][/tex]
So, we have [tex]\(|x|\)[/tex] because the square root of [tex]\(x^2\)[/tex] is [tex]\(x\)[/tex] in absolute terms (it can be both positive or negative).
- For [tex]\(\sqrt{y^6}\)[/tex]:
[tex]\[\sqrt{y^6} = y^3\][/tex]
This follows because [tex]\((y^3)^2 = y^6\)[/tex], so the square root of [tex]\(y^6\)[/tex] is [tex]\(y^3\)[/tex].
5. Combine the Simplified Parts:
Putting these together, we get:
[tex]\[\sqrt{x^2 y^6} = |x| \cdot y^3\][/tex]
Hence, the simplified form of [tex]\(\sqrt{x^2 y^6}\)[/tex] is:
[tex]\[|x| y^3\][/tex]
1. Understand the Expression Inside the Square Root:
The expression inside the square root is [tex]\(x^2 y^6\)[/tex].
2. Break Down the Terms:
We can break down the terms inside the square root based on their properties:
[tex]\[\sqrt{x^2 y^6} = \sqrt{x^2 \cdot y^6}\][/tex]
3. Apply the Square Root to Each Part:
The square root of a product is the product of the square roots:
[tex]\[\sqrt{x^2 \cdot y^6} = \sqrt{x^2} \cdot \sqrt{y^6}\][/tex]
4. Simplify Each Square Root Separately:
- For [tex]\(\sqrt{x^2}\)[/tex]:
[tex]\[\sqrt{x^2} = |x|\][/tex]
So, we have [tex]\(|x|\)[/tex] because the square root of [tex]\(x^2\)[/tex] is [tex]\(x\)[/tex] in absolute terms (it can be both positive or negative).
- For [tex]\(\sqrt{y^6}\)[/tex]:
[tex]\[\sqrt{y^6} = y^3\][/tex]
This follows because [tex]\((y^3)^2 = y^6\)[/tex], so the square root of [tex]\(y^6\)[/tex] is [tex]\(y^3\)[/tex].
5. Combine the Simplified Parts:
Putting these together, we get:
[tex]\[\sqrt{x^2 y^6} = |x| \cdot y^3\][/tex]
Hence, the simplified form of [tex]\(\sqrt{x^2 y^6}\)[/tex] is:
[tex]\[|x| y^3\][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.