Lesson Example Discussion Quiz: Class Homework |
Step-1 |
Title: Dividing Radicals |
Grade: 8-b Lesson: S1-L8 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Dividing the following radical expression: \$ 3/ (\sqrt(5) + \sqrt(2))\$. |
|
2 |
Step |
The given expression is |
\$ 3/ (\sqrt(5) + \sqrt(2))\$ |
3 |
Step |
Multiply the numerator and the denominator by the conjugate of the denominator: |
\$ 3/ (\sqrt(5) + \sqrt(2)) times (\sqrt(5) - \sqrt(2)) / (\sqrt(5) - \sqrt(2))\$ \$(3(\sqrt(5) - \sqrt(2))) / ((sqrt(5))^2 - (\sqrt(2))^2)\$ |
4 |
Step |
Simplify the denominator: |
\$(\sqrt(5))^2 - (\sqrt(2))^2 = 5 - 2 = 3\$ |
5 |
Step |
Combine the results: |
\$ (3 (\sqrt(5) - \sqrt(2))) /3\$ |
6 |
Step |
Simplify the expression: |
\$\sqrt(5) - \sqrt(2)\$ |
7 |
Step |
Therefore, the simplified expression is \$\sqrt(5) - \sqrt(2)\$. |
|
8 |
Choice.A |
\$\sqrt(3) - \sqrt(2)\$ wrong: The correct conjugate to rationalize the denominator involves \$\sqrt(5)\$ not \$\sqrt(3)\$ |
\$\sqrt(3) - \sqrt(2)\$ |
9 |
Choice.B |
Option B does not represent the correctly rationalized form of the given expression |
\$\sqrt(5) + \sqrt(2)\$ |
10 |
Choice.C |
Option C would not result from this rationalization process because the terms involve \$\sqrt(5)\$ not \$\sqrt(3)\$ |
\$\sqrt(3) + \sqrt(2)\$ |
11 |
Choice.D |
Option D is correct because after rationalizing the denominator, the expression simplifies to \$\sqrt(5) - \sqrt(2)\$ |
\$\sqrt(5) - \sqrt(2)\$ |
12 |
Answer |
Option |
D |
13 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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