Find solutions to your questions with the help of IDNLearn.com's expert community. Ask anything and get well-informed, reliable answers from our knowledgeable community members.
Sagot :
Given the expressions [tex]\(\sqrt{60}\)[/tex] and [tex]\(\sqrt{114}\)[/tex], we want to find their simplified forms.
1. Simplifying [tex]\(\sqrt{60}\)[/tex]:
- The number 60 can be factored into prime factors: [tex]\(60 = 2^2 \cdot 3 \cdot 5\)[/tex].
- Using the property of square roots, we can separate the factors: [tex]\(\sqrt{60} = \sqrt{2^2 \cdot 3 \cdot 5}\)[/tex].
- We know that [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex], so we can write: [tex]\(\sqrt{60} = \sqrt{2^2} \cdot \sqrt{3 \cdot 5}\)[/tex].
- Simplifying further, [tex]\(\sqrt{2^2} = 2\)[/tex], so [tex]\(\sqrt{60} = 2 \cdot \sqrt{15}\)[/tex].
Therefore, [tex]\(\sqrt{60} = 2\sqrt{15}\)[/tex].
2. Simplifying [tex]\(\sqrt{114}\)[/tex]:
- The number 114 can be factored into prime factors: [tex]\(114 = 2 \cdot 3 \cdot 19\)[/tex].
- Using the property of square roots, we can separate the factors: [tex]\(\sqrt{114} = \sqrt{2 \cdot 3 \cdot 19}\)[/tex].
- Each of the factors (2, 3, and 19) is a prime number and cannot be simplified further under the square root.
Therefore, [tex]\(\sqrt{114}\)[/tex] remains as [tex]\(\sqrt{114}\)[/tex].
In conclusion, the simplified forms of the given expressions are:
[tex]\[ \sqrt{60} = 2\sqrt{15} \][/tex]
[tex]\[ \sqrt{114} = \sqrt{114} \][/tex]
1. Simplifying [tex]\(\sqrt{60}\)[/tex]:
- The number 60 can be factored into prime factors: [tex]\(60 = 2^2 \cdot 3 \cdot 5\)[/tex].
- Using the property of square roots, we can separate the factors: [tex]\(\sqrt{60} = \sqrt{2^2 \cdot 3 \cdot 5}\)[/tex].
- We know that [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex], so we can write: [tex]\(\sqrt{60} = \sqrt{2^2} \cdot \sqrt{3 \cdot 5}\)[/tex].
- Simplifying further, [tex]\(\sqrt{2^2} = 2\)[/tex], so [tex]\(\sqrt{60} = 2 \cdot \sqrt{15}\)[/tex].
Therefore, [tex]\(\sqrt{60} = 2\sqrt{15}\)[/tex].
2. Simplifying [tex]\(\sqrt{114}\)[/tex]:
- The number 114 can be factored into prime factors: [tex]\(114 = 2 \cdot 3 \cdot 19\)[/tex].
- Using the property of square roots, we can separate the factors: [tex]\(\sqrt{114} = \sqrt{2 \cdot 3 \cdot 19}\)[/tex].
- Each of the factors (2, 3, and 19) is a prime number and cannot be simplified further under the square root.
Therefore, [tex]\(\sqrt{114}\)[/tex] remains as [tex]\(\sqrt{114}\)[/tex].
In conclusion, the simplified forms of the given expressions are:
[tex]\[ \sqrt{60} = 2\sqrt{15} \][/tex]
[tex]\[ \sqrt{114} = \sqrt{114} \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.