Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To simplify the radical [tex]\(\sqrt{50}\)[/tex], we start by breaking down 50 into its prime factors.
The number 50 can be factored as [tex]\(50 = 25 \times 2\)[/tex]. Notice that 25 is a perfect square. We can then rewrite the square root of 50 using these factors:
[tex]\[ \sqrt{50} = \sqrt{25 \times 2} \][/tex]
Using the property of square roots that allows us to separate the factors, we have:
[tex]\[ \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} \][/tex]
Since [tex]\(\sqrt{25}\)[/tex] is 5 (because [tex]\(5^2 = 25\)[/tex]), we can simplify further:
[tex]\[ \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[ 5 \sqrt{2} \][/tex]
The correct answer from the given choices is:
D. [tex]\(5 \sqrt{2}\)[/tex]
For verification, converting [tex]\(5 \sqrt{2}\)[/tex] to a numerical form, we get approximately 7.0710678118654755. This confirms that our simplified radical form is correct.
The number 50 can be factored as [tex]\(50 = 25 \times 2\)[/tex]. Notice that 25 is a perfect square. We can then rewrite the square root of 50 using these factors:
[tex]\[ \sqrt{50} = \sqrt{25 \times 2} \][/tex]
Using the property of square roots that allows us to separate the factors, we have:
[tex]\[ \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} \][/tex]
Since [tex]\(\sqrt{25}\)[/tex] is 5 (because [tex]\(5^2 = 25\)[/tex]), we can simplify further:
[tex]\[ \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[ 5 \sqrt{2} \][/tex]
The correct answer from the given choices is:
D. [tex]\(5 \sqrt{2}\)[/tex]
For verification, converting [tex]\(5 \sqrt{2}\)[/tex] to a numerical form, we get approximately 7.0710678118654755. This confirms that our simplified radical form is correct.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.