Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Discover prompt and accurate answers from our community of experienced professionals.
Sagot :
Sure, let's go through the given problem step by step.
We start with the given value:
[tex]\[ x = 5 + 2\sqrt{6} \][/tex]
The next step involves taking the square root of [tex]\( x \)[/tex]:
[tex]\[ \sqrt{x} = \sqrt{5 + 2\sqrt{6}} \][/tex]
Let's assume [tex]\(\sqrt{x}\)[/tex] is approximately equal to some value. According to the precise numerical result:
[tex]\[ \sqrt{x} \approx 3.146264369941972 \][/tex]
Now, we need to compute the reciprocal of [tex]\(\sqrt{x}\)[/tex] and calculate the following expression:
[tex]\[ \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right) \][/tex]
Given the value of [tex]\(\sqrt{x}\)[/tex] is approximately [tex]\( 3.146264369941972 \)[/tex], we find:
[tex]\[ \frac{1}{\sqrt{x}} \approx \frac{1}{3.146264369941972} \][/tex]
The numerical result already tells us that:
[tex]\[ \sqrt{x} - \frac{1}{\sqrt{x}} \approx 2.82842712474619 \][/tex]
Given the result:
[tex]\[ \sqrt{x} - \frac{1}{\sqrt{x}} \approx 2.82842712474619 \][/tex]
We can identify that this value corresponds to:
[tex]\[\sqrt{8} = 2\sqrt{2} \][/tex]
Thus, the value of the given expression is:
[tex]\[ \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right) \approx 2\sqrt{2} \][/tex]
Hence, the correct answer is:
[tex]\[ B. \, 2\sqrt{2} \][/tex]
We start with the given value:
[tex]\[ x = 5 + 2\sqrt{6} \][/tex]
The next step involves taking the square root of [tex]\( x \)[/tex]:
[tex]\[ \sqrt{x} = \sqrt{5 + 2\sqrt{6}} \][/tex]
Let's assume [tex]\(\sqrt{x}\)[/tex] is approximately equal to some value. According to the precise numerical result:
[tex]\[ \sqrt{x} \approx 3.146264369941972 \][/tex]
Now, we need to compute the reciprocal of [tex]\(\sqrt{x}\)[/tex] and calculate the following expression:
[tex]\[ \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right) \][/tex]
Given the value of [tex]\(\sqrt{x}\)[/tex] is approximately [tex]\( 3.146264369941972 \)[/tex], we find:
[tex]\[ \frac{1}{\sqrt{x}} \approx \frac{1}{3.146264369941972} \][/tex]
The numerical result already tells us that:
[tex]\[ \sqrt{x} - \frac{1}{\sqrt{x}} \approx 2.82842712474619 \][/tex]
Given the result:
[tex]\[ \sqrt{x} - \frac{1}{\sqrt{x}} \approx 2.82842712474619 \][/tex]
We can identify that this value corresponds to:
[tex]\[\sqrt{8} = 2\sqrt{2} \][/tex]
Thus, the value of the given expression is:
[tex]\[ \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right) \approx 2\sqrt{2} \][/tex]
Hence, the correct answer is:
[tex]\[ B. \, 2\sqrt{2} \][/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. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.