Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Alright, let's simplify the expression [tex]\(\frac{2 a}{\sqrt{2 a x}}\)[/tex] step by step.
1. Start with the original expression:
[tex]\[ \frac{2 a}{\sqrt{2 a x}} \][/tex]
2. Observe that the terms inside the square root can be separated into their individual square roots:
[tex]\[ \sqrt{2 a x} = \sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x} \][/tex]
Thus, the expression becomes:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} \][/tex]
3. Separate the terms in the numerator and the denominator:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} = \frac{2 a}{\sqrt{2} \sqrt{a} \sqrt{x}} = \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} \][/tex]
4. Simplify the fraction by dividing [tex]\(2a\)[/tex] by [tex]\(\sqrt{a}\)[/tex]:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} = \frac{2 \cdot a}{\sqrt{a}} \cdot \frac{1}{\sqrt{2} \sqrt{x}} \][/tex]
5. Simplify [tex]\(\frac{a}{\sqrt{a}}\)[/tex]:
[tex]\[ \frac{a}{\sqrt{a}} = \frac{a \cdot a^{-1/2}}{1} = \frac{a^{1}}{a^{1/2}} = a^{1 - 1/2} = a^{1/2} \][/tex]
So, the expression becomes:
[tex]\[ \frac{2 \cdot a^{1/2}}{\sqrt{2} \cdot \sqrt{x}} = \frac{2 \cdot \sqrt{a}}{\sqrt{2} \cdot \sqrt{x}} \][/tex]
6. Simplify [tex]\(\frac{2}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{2}{\sqrt{2}} = \frac{2}{2^{1/2}} = 2^{1 - 1/2} = 2^{1/2} = \sqrt{2} \][/tex]
7. Combine all the simplified terms:
[tex]\[ \frac{\sqrt{2} \cdot \sqrt{a}}{\sqrt{x}} = \frac{\sqrt{2a}}{\sqrt{x}} \][/tex]
Thus, the simplified expression is:
[tex]\[ \frac{\sqrt{2} \cdot \sqrt{a}}{\sqrt{x}} \][/tex]
1. Start with the original expression:
[tex]\[ \frac{2 a}{\sqrt{2 a x}} \][/tex]
2. Observe that the terms inside the square root can be separated into their individual square roots:
[tex]\[ \sqrt{2 a x} = \sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x} \][/tex]
Thus, the expression becomes:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} \][/tex]
3. Separate the terms in the numerator and the denominator:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} = \frac{2 a}{\sqrt{2} \sqrt{a} \sqrt{x}} = \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} \][/tex]
4. Simplify the fraction by dividing [tex]\(2a\)[/tex] by [tex]\(\sqrt{a}\)[/tex]:
[tex]\[ \frac{2 a}{\sqrt{2} \cdot \sqrt{a} \cdot \sqrt{x}} = \frac{2 \cdot a}{\sqrt{a}} \cdot \frac{1}{\sqrt{2} \sqrt{x}} \][/tex]
5. Simplify [tex]\(\frac{a}{\sqrt{a}}\)[/tex]:
[tex]\[ \frac{a}{\sqrt{a}} = \frac{a \cdot a^{-1/2}}{1} = \frac{a^{1}}{a^{1/2}} = a^{1 - 1/2} = a^{1/2} \][/tex]
So, the expression becomes:
[tex]\[ \frac{2 \cdot a^{1/2}}{\sqrt{2} \cdot \sqrt{x}} = \frac{2 \cdot \sqrt{a}}{\sqrt{2} \cdot \sqrt{x}} \][/tex]
6. Simplify [tex]\(\frac{2}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{2}{\sqrt{2}} = \frac{2}{2^{1/2}} = 2^{1 - 1/2} = 2^{1/2} = \sqrt{2} \][/tex]
7. Combine all the simplified terms:
[tex]\[ \frac{\sqrt{2} \cdot \sqrt{a}}{\sqrt{x}} = \frac{\sqrt{2a}}{\sqrt{x}} \][/tex]
Thus, the simplified expression is:
[tex]\[ \frac{\sqrt{2} \cdot \sqrt{a}}{\sqrt{x}} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.