From personal advice to professional guidance, IDNLearn.com has the answers you seek. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.
Sagot :
To simplify the radical expression [tex]\(\sqrt{20}\)[/tex], we need to look for perfect square factors of 20. Here’s the detailed step-by-step process:
1. Identify factors of 20:
The number 20 can be factored into [tex]\( 4 \times 5 \)[/tex].
2. Simplify the square root:
Since 4 is a perfect square ([tex]\(4 = 2^2\)[/tex]), we can split the expression using the properties of square roots:
[tex]\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} \][/tex]
3. Calculate the square root of the perfect square:
We know that [tex]\(\sqrt{4} = 2\)[/tex], so substituting this in:
[tex]\[ \sqrt{4} \times \sqrt{5} = 2 \times \sqrt{5} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{20}\)[/tex] is:
[tex]\[ 2 \sqrt{5} \][/tex]
Thus, the correct answer is [tex]\( \boxed{2 \sqrt{5}} \)[/tex].
1. Identify factors of 20:
The number 20 can be factored into [tex]\( 4 \times 5 \)[/tex].
2. Simplify the square root:
Since 4 is a perfect square ([tex]\(4 = 2^2\)[/tex]), we can split the expression using the properties of square roots:
[tex]\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} \][/tex]
3. Calculate the square root of the perfect square:
We know that [tex]\(\sqrt{4} = 2\)[/tex], so substituting this in:
[tex]\[ \sqrt{4} \times \sqrt{5} = 2 \times \sqrt{5} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{20}\)[/tex] is:
[tex]\[ 2 \sqrt{5} \][/tex]
Thus, the correct answer is [tex]\( \boxed{2 \sqrt{5}} \)[/tex].
We 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. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.