Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Certainly! Let's break down each part of the problem step by step and resolve the equations.
1. Resolving the fourth root of 81:
[tex]\[ \sqrt[4]{81} \][/tex]
To find the fourth root of 81, we look for a number which, when raised to the power of 4, equals 81. The correct value is 3, because [tex]\(3^4 = 81\)[/tex].
[tex]\[ \sqrt[4]{81} = 3 \][/tex]
2. Calculating [tex]\(-\sqrt{9 \times 9}\)[/tex]:
[tex]\[ -\sqrt{9 \times 9} \][/tex]
First, calculate [tex]\(9 \times 9\)[/tex]:
[tex]\[ 9 \times 9 = 81 \][/tex]
Then, find the square root of 81:
[tex]\[ \sqrt{81} = 9 \][/tex]
Finally, apply the negative sign:
[tex]\[ -\sqrt{81} = -9 \][/tex]
3. Resolving the cube root of 64:
[tex]\[ \sqrt[3]{64} \][/tex]
To find the cube root of 64, we look for a number which, when raised to the power of 3, equals 64. The correct value is approximately 4.
So,
[tex]\[ \sqrt[3]{64} \approx 4 \][/tex]
4. Resolving the fifth root of 64:
[tex]\[ \sqrt[5]{64} \][/tex]
To find the fifth root of 64, we look for a number which, when raised to the power of 5, equals 64. The result is approximately 2.297.
So,
[tex]\[ \sqrt[5]{64} \approx 2.297 \][/tex]
5. Calculating the square root of 125:
[tex]\[ \sqrt{125} \][/tex]
The square root of 125 is approximately 11.180.
Thus,
[tex]\[ \sqrt{125} \approx 11.180 \][/tex]
Combining all results together, we have:
[tex]\[ \begin{aligned} \sqrt[4]{81} & = 3, \\ -\sqrt{9 \times 9} & = -9, \\ \sqrt[3]{64} & \approx 4, \\ \sqrt[5]{64} & \approx 2.297, \\ \sqrt{125} & \approx 11.180. \end{aligned} \][/tex]
These are the step-by-step solutions to the given mathematical expressions.
1. Resolving the fourth root of 81:
[tex]\[ \sqrt[4]{81} \][/tex]
To find the fourth root of 81, we look for a number which, when raised to the power of 4, equals 81. The correct value is 3, because [tex]\(3^4 = 81\)[/tex].
[tex]\[ \sqrt[4]{81} = 3 \][/tex]
2. Calculating [tex]\(-\sqrt{9 \times 9}\)[/tex]:
[tex]\[ -\sqrt{9 \times 9} \][/tex]
First, calculate [tex]\(9 \times 9\)[/tex]:
[tex]\[ 9 \times 9 = 81 \][/tex]
Then, find the square root of 81:
[tex]\[ \sqrt{81} = 9 \][/tex]
Finally, apply the negative sign:
[tex]\[ -\sqrt{81} = -9 \][/tex]
3. Resolving the cube root of 64:
[tex]\[ \sqrt[3]{64} \][/tex]
To find the cube root of 64, we look for a number which, when raised to the power of 3, equals 64. The correct value is approximately 4.
So,
[tex]\[ \sqrt[3]{64} \approx 4 \][/tex]
4. Resolving the fifth root of 64:
[tex]\[ \sqrt[5]{64} \][/tex]
To find the fifth root of 64, we look for a number which, when raised to the power of 5, equals 64. The result is approximately 2.297.
So,
[tex]\[ \sqrt[5]{64} \approx 2.297 \][/tex]
5. Calculating the square root of 125:
[tex]\[ \sqrt{125} \][/tex]
The square root of 125 is approximately 11.180.
Thus,
[tex]\[ \sqrt{125} \approx 11.180 \][/tex]
Combining all results together, we have:
[tex]\[ \begin{aligned} \sqrt[4]{81} & = 3, \\ -\sqrt{9 \times 9} & = -9, \\ \sqrt[3]{64} & \approx 4, \\ \sqrt[5]{64} & \approx 2.297, \\ \sqrt{125} & \approx 11.180. \end{aligned} \][/tex]
These are the step-by-step solutions to the given mathematical expressions.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.