Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Certainly! Let's analyze each expression to determine if it is equivalent to [tex]\(\sqrt{40}\)[/tex].
1. First Expression: [tex]\(\sqrt{40}\)[/tex]
We start with the given expression:
[tex]\[ \sqrt{40} \][/tex]
To simplify this, we need to look at the prime factors of 40:
[tex]\[ 40 = 4 \times 10 = 2^2 \times 10 \][/tex]
Therefore,
[tex]\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \][/tex]
So, [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex]. This means [tex]\(\sqrt{40}\)[/tex] is equivalent to [tex]\(2\sqrt{10}\)[/tex].
2. Second Expression: [tex]\(40 \frac{1}{\frac{1}{2}}\)[/tex]
Simplify the fraction inside the expression:
[tex]\[ \frac{1}{\frac{1}{2}} = 2 \][/tex]
Therefore,
[tex]\[ 40 \times 2 = 80 \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 80 \neq 2\sqrt{10} \][/tex]
So, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
3. Third Expression: [tex]\(2 \sqrt{10}\)[/tex]
We already know from our simplification that:
[tex]\[ \sqrt{40} = 2\sqrt{10} \][/tex]
Therefore, [tex]\(2\sqrt{10}\)[/tex] is equivalent to [tex]\(\sqrt{40}\)[/tex].
4. Fourth Expression: [tex]\(5 \sqrt{8}\)[/tex]
Let's simplify [tex]\(5 \sqrt{8}\)[/tex]:
[tex]\[ 8 = 4 \times 2 = 2^3 \][/tex]
Therefore,
[tex]\[ \sqrt{8} = \sqrt{2^3} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \][/tex]
So,
[tex]\[ 5 \sqrt{8} = 5 \times 2 \sqrt{2} = 10 \sqrt{2} \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 10 \sqrt{2} \neq 2 \sqrt{10} \][/tex]
Hence, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
5. Fifth Expression: [tex]\(4 \sqrt{10}\)[/tex]
Simplifying [tex]\(4 \sqrt{10}\)[/tex] as it is:
[tex]\[ 4 \sqrt{10} \][/tex]
Since we already have:
[tex]\[ 2 \sqrt{10} \neq 4 \sqrt{10} \][/tex]
So, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
6. Sixth Expression: [tex]\(160^{\frac{1}{2}}\)[/tex]
Simplify [tex]\(160^{\frac{1}{2}}\)[/tex]:
[tex]\[ \sqrt{160} \][/tex]
We know:
[tex]\[ 160 = 16 \times 10 = (4^2 \times 10) \][/tex]
So,
[tex]\[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 4 \sqrt{10} \neq 2 \sqrt{10} \][/tex]
Therefore, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
Based on this detailed analysis, the expressions equivalent to [tex]\(\sqrt{40}\)[/tex] are:
[tex]\(2 \sqrt{10}\)[/tex].
1. First Expression: [tex]\(\sqrt{40}\)[/tex]
We start with the given expression:
[tex]\[ \sqrt{40} \][/tex]
To simplify this, we need to look at the prime factors of 40:
[tex]\[ 40 = 4 \times 10 = 2^2 \times 10 \][/tex]
Therefore,
[tex]\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \][/tex]
So, [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex]. This means [tex]\(\sqrt{40}\)[/tex] is equivalent to [tex]\(2\sqrt{10}\)[/tex].
2. Second Expression: [tex]\(40 \frac{1}{\frac{1}{2}}\)[/tex]
Simplify the fraction inside the expression:
[tex]\[ \frac{1}{\frac{1}{2}} = 2 \][/tex]
Therefore,
[tex]\[ 40 \times 2 = 80 \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 80 \neq 2\sqrt{10} \][/tex]
So, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
3. Third Expression: [tex]\(2 \sqrt{10}\)[/tex]
We already know from our simplification that:
[tex]\[ \sqrt{40} = 2\sqrt{10} \][/tex]
Therefore, [tex]\(2\sqrt{10}\)[/tex] is equivalent to [tex]\(\sqrt{40}\)[/tex].
4. Fourth Expression: [tex]\(5 \sqrt{8}\)[/tex]
Let's simplify [tex]\(5 \sqrt{8}\)[/tex]:
[tex]\[ 8 = 4 \times 2 = 2^3 \][/tex]
Therefore,
[tex]\[ \sqrt{8} = \sqrt{2^3} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \][/tex]
So,
[tex]\[ 5 \sqrt{8} = 5 \times 2 \sqrt{2} = 10 \sqrt{2} \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 10 \sqrt{2} \neq 2 \sqrt{10} \][/tex]
Hence, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
5. Fifth Expression: [tex]\(4 \sqrt{10}\)[/tex]
Simplifying [tex]\(4 \sqrt{10}\)[/tex] as it is:
[tex]\[ 4 \sqrt{10} \][/tex]
Since we already have:
[tex]\[ 2 \sqrt{10} \neq 4 \sqrt{10} \][/tex]
So, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
6. Sixth Expression: [tex]\(160^{\frac{1}{2}}\)[/tex]
Simplify [tex]\(160^{\frac{1}{2}}\)[/tex]:
[tex]\[ \sqrt{160} \][/tex]
We know:
[tex]\[ 160 = 16 \times 10 = (4^2 \times 10) \][/tex]
So,
[tex]\[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \][/tex]
Comparing this with our simplified [tex]\(\sqrt{40}\)[/tex]:
[tex]\[ 4 \sqrt{10} \neq 2 \sqrt{10} \][/tex]
Therefore, this expression is not equivalent to [tex]\(\sqrt{40}\)[/tex].
Based on this detailed analysis, the expressions equivalent to [tex]\(\sqrt{40}\)[/tex] are:
[tex]\(2 \sqrt{10}\)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
