Find expert answers and community insights on IDNLearn.com. Discover reliable answers to your questions with our extensive database of expert knowledge.
Sagot :
To simplify the expression [tex]\(\sqrt{48 y^{14}}\)[/tex], let's proceed step-by-step:
1. Express the radicand as a product of perfect squares and other factors:
Recognize that [tex]\(48\)[/tex] can be factored into [tex]\(16 \times 3\)[/tex], where [tex]\(16\)[/tex] is a perfect square:
[tex]\[ 48 = 16 \times 3 \][/tex]
So the expression becomes:
[tex]\[ \sqrt{48 y^{14}} = \sqrt{16 \times 3 \times y^{14}} \][/tex]
2. Separate the square roots of each factor:
Use the property of square roots [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[ \sqrt{16 \times 3 \times y^{14}} = \sqrt{16} \times \sqrt{3} \times \sqrt{y^{14}} \][/tex]
3. Take the square root of the perfect square numbers and even powers:
- The square root of [tex]\(16\)[/tex] is [tex]\(4\)[/tex]:
[tex]\[ \sqrt{16} = 4 \][/tex]
- For [tex]\(y^{14}\)[/tex], since [tex]\(14\)[/tex] is an even number, the square root simply halves the exponent:
[tex]\[ \sqrt{y^{14}} = y^{14/2} = y^7 \][/tex]
4. Combine all the simplified components:
Now, put all the simplified parts together:
[tex]\[ \sqrt{16} \times \sqrt{3} \times \sqrt{y^{14}} = 4 \times \sqrt{3} \times y^7 \][/tex]
Therefore, the simplified form of the expression [tex]\(\sqrt{48 y^{14}}\)[/tex] is:
[tex]\[ 4 \sqrt{3} y^7 \][/tex]
This completes the simplification process.
1. Express the radicand as a product of perfect squares and other factors:
Recognize that [tex]\(48\)[/tex] can be factored into [tex]\(16 \times 3\)[/tex], where [tex]\(16\)[/tex] is a perfect square:
[tex]\[ 48 = 16 \times 3 \][/tex]
So the expression becomes:
[tex]\[ \sqrt{48 y^{14}} = \sqrt{16 \times 3 \times y^{14}} \][/tex]
2. Separate the square roots of each factor:
Use the property of square roots [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[ \sqrt{16 \times 3 \times y^{14}} = \sqrt{16} \times \sqrt{3} \times \sqrt{y^{14}} \][/tex]
3. Take the square root of the perfect square numbers and even powers:
- The square root of [tex]\(16\)[/tex] is [tex]\(4\)[/tex]:
[tex]\[ \sqrt{16} = 4 \][/tex]
- For [tex]\(y^{14}\)[/tex], since [tex]\(14\)[/tex] is an even number, the square root simply halves the exponent:
[tex]\[ \sqrt{y^{14}} = y^{14/2} = y^7 \][/tex]
4. Combine all the simplified components:
Now, put all the simplified parts together:
[tex]\[ \sqrt{16} \times \sqrt{3} \times \sqrt{y^{14}} = 4 \times \sqrt{3} \times y^7 \][/tex]
Therefore, the simplified form of the expression [tex]\(\sqrt{48 y^{14}}\)[/tex] is:
[tex]\[ 4 \sqrt{3} y^7 \][/tex]
This completes the simplification process.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.