Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To solve the expression [tex]\(-\sqrt{\frac{-7}{4}} - \sqrt{\frac{-1}{7}}\)[/tex], let's break it down into two parts.
1. First term: [tex]\(-\sqrt{\frac{-7}{4}}\)[/tex]:
- The expression inside the square root is [tex]\(\frac{-7}{4}\)[/tex], which is a negative fraction.
- Taking the square root of a negative number introduces an imaginary unit, [tex]\(i\)[/tex].
- Therefore, [tex]\(\sqrt{\frac{-7}{4}}\)[/tex] can be re-written as [tex]\(\sqrt{\frac{7}{4}} \cdot i\)[/tex].
Now let's calculate [tex]\(\sqrt{\frac{7}{4}}\)[/tex]:
- [tex]\(\sqrt{\frac{7}{4}} = \frac{\sqrt{7}}{\sqrt{4}} = \frac{\sqrt{7}}{2}\)[/tex]
- Thus, [tex]\(\sqrt{\frac{-7}{4}} = \frac{\sqrt{7}}{2} \cdot i\)[/tex]
- Finally, we apply the negative sign: [tex]\(-\sqrt{\frac{-7}{4}} = -\frac{\sqrt{7}}{2} \cdot i\)[/tex]
2. Second term: [tex]\(-\sqrt{\frac{-1}{7}}\)[/tex]:
- The expression inside the square root is [tex]\(\frac{-1}{7}\)[/tex], also a negative fraction.
- As before, the square root of a negative number introduces an imaginary unit, [tex]\(i\)[/tex].
- So [tex]\(\sqrt{\frac{-1}{7}}\)[/tex] becomes [tex]\(\sqrt{\frac{1}{7}} \cdot i\)[/tex].
Now let's calculate [tex]\(\sqrt{\frac{1}{7}}\)[/tex]:
- [tex]\(\sqrt{\frac{1}{7}} = \sqrt{1} / \sqrt{7} = \frac{1}{\sqrt{7}} = \frac{\sqrt{7}}{7}\)[/tex] (by rationalizing the denominator)
- Thus, [tex]\(\sqrt{\frac{-1}{7}} = \frac{\sqrt{7}}{7} \cdot i\)[/tex]
- Finally, we apply the negative sign: [tex]\(-\sqrt{\frac{-1}{7}} = -\frac{\sqrt{7}}{7} \cdot i\)[/tex]
3. Combining the results:
- The first term calculated was [tex]\(-\frac{\sqrt{7}}{2} \cdot i\)[/tex]
- The second term calculated was [tex]\(-\frac{\sqrt{7}}{7} \cdot i\)[/tex]
Bringing both terms together, we have:
[tex]\[ -\frac{\sqrt{7}}{2} \cdot i - \frac{\sqrt{7}}{7} \cdot i \][/tex]
Given the calculated results, the expressions are:
[tex]\[ -\frac{\sqrt{7}}{2} \cdot i \approx (-8.100277186087911e-17 - 1.3228756555322954j) \][/tex]
and
[tex]\[ -\frac{\sqrt{7}}{7} \cdot i \approx (-2.3143649103108314e-17 - 0.3779644730092272j) \][/tex]
The overall result by combining these two terms will be:
[tex]\[ (-8.100277186087911e-17 - 1.3228756555322954j) + (-2.3143649103108314e-17 - 0.3779644730092272j) \][/tex]
[tex]\[ = (-1.0414642096398742e-16 - 1.7008401285415226j) \][/tex]
Hence, the final answer for [tex]\(-\sqrt{\frac{-7}{4}} - \sqrt{\frac{-1}{7}}\)[/tex] is:
[tex]\[ (-1.0414642096398742e-16 - 1.7008401285415226j) \][/tex]
1. First term: [tex]\(-\sqrt{\frac{-7}{4}}\)[/tex]:
- The expression inside the square root is [tex]\(\frac{-7}{4}\)[/tex], which is a negative fraction.
- Taking the square root of a negative number introduces an imaginary unit, [tex]\(i\)[/tex].
- Therefore, [tex]\(\sqrt{\frac{-7}{4}}\)[/tex] can be re-written as [tex]\(\sqrt{\frac{7}{4}} \cdot i\)[/tex].
Now let's calculate [tex]\(\sqrt{\frac{7}{4}}\)[/tex]:
- [tex]\(\sqrt{\frac{7}{4}} = \frac{\sqrt{7}}{\sqrt{4}} = \frac{\sqrt{7}}{2}\)[/tex]
- Thus, [tex]\(\sqrt{\frac{-7}{4}} = \frac{\sqrt{7}}{2} \cdot i\)[/tex]
- Finally, we apply the negative sign: [tex]\(-\sqrt{\frac{-7}{4}} = -\frac{\sqrt{7}}{2} \cdot i\)[/tex]
2. Second term: [tex]\(-\sqrt{\frac{-1}{7}}\)[/tex]:
- The expression inside the square root is [tex]\(\frac{-1}{7}\)[/tex], also a negative fraction.
- As before, the square root of a negative number introduces an imaginary unit, [tex]\(i\)[/tex].
- So [tex]\(\sqrt{\frac{-1}{7}}\)[/tex] becomes [tex]\(\sqrt{\frac{1}{7}} \cdot i\)[/tex].
Now let's calculate [tex]\(\sqrt{\frac{1}{7}}\)[/tex]:
- [tex]\(\sqrt{\frac{1}{7}} = \sqrt{1} / \sqrt{7} = \frac{1}{\sqrt{7}} = \frac{\sqrt{7}}{7}\)[/tex] (by rationalizing the denominator)
- Thus, [tex]\(\sqrt{\frac{-1}{7}} = \frac{\sqrt{7}}{7} \cdot i\)[/tex]
- Finally, we apply the negative sign: [tex]\(-\sqrt{\frac{-1}{7}} = -\frac{\sqrt{7}}{7} \cdot i\)[/tex]
3. Combining the results:
- The first term calculated was [tex]\(-\frac{\sqrt{7}}{2} \cdot i\)[/tex]
- The second term calculated was [tex]\(-\frac{\sqrt{7}}{7} \cdot i\)[/tex]
Bringing both terms together, we have:
[tex]\[ -\frac{\sqrt{7}}{2} \cdot i - \frac{\sqrt{7}}{7} \cdot i \][/tex]
Given the calculated results, the expressions are:
[tex]\[ -\frac{\sqrt{7}}{2} \cdot i \approx (-8.100277186087911e-17 - 1.3228756555322954j) \][/tex]
and
[tex]\[ -\frac{\sqrt{7}}{7} \cdot i \approx (-2.3143649103108314e-17 - 0.3779644730092272j) \][/tex]
The overall result by combining these two terms will be:
[tex]\[ (-8.100277186087911e-17 - 1.3228756555322954j) + (-2.3143649103108314e-17 - 0.3779644730092272j) \][/tex]
[tex]\[ = (-1.0414642096398742e-16 - 1.7008401285415226j) \][/tex]
Hence, the final answer for [tex]\(-\sqrt{\frac{-7}{4}} - \sqrt{\frac{-1}{7}}\)[/tex] is:
[tex]\[ (-1.0414642096398742e-16 - 1.7008401285415226j) \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
