Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Multiplying Radicals |
Grade: 8-b Lesson: S1-L7 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Simplify: \$(2\sqrt(5) + 3\sqrt(2)) times \$ (\$\sqrt(5) - \sqrt(2)\$). |
|
2 |
Step |
Given expression |
\$(2\sqrt(5) + 3\sqrt(2)) times \$ (\$\sqrt(5) - \sqrt(2)\$) |
3 |
Step |
Expand using the distributive property: |
\$(2\sqrt(5) + 3\sqrt(2)) \times (\sqrt(5) - \sqrt(2))\$ \$2\sqrt(5) \times \sqrt(5) - 2\sqrt(5) \times \sqrt(2) + 3\sqrt(2) \times \sqrt(5) - 3\sqrt(2) \times \sqrt(2)\$ |
4 |
Step |
Simplify each term: |
\$2\sqrt(5) \times \sqrt(5) = 2 \times 5 = 10\$ \$-2\sqrt(5) \times \sqrt(2) = -2\sqrt(10)\$ \$3\sqrt(2) \times \sqrt(5) = 3\sqrt(10)\$ \$-3\sqrt(2) \times \sqrt(2) = -3 \times 2 = -6\$ |
5 |
Step |
Combine like terms: |
\$10 - 2\sqrt(10) + 3\sqrt(10) - 6 = 4 + \sqrt(10)\$ |
6 |
Step |
Therefore, the simplified expression is \$4 + \sqrt(10)\$. |
|
7 |
Choice.A |
This option matches our simplified expression \$4 + \sqrt(10)\$ |
\$4 + \sqrt(10)\$ |
8 |
Choice.B |
This option is not correct, as our simplified expression does not involve \$\sqrt(12)\$ |
\$4 + \sqrt(12)\$ |
9 |
Choice.C |
This option is not correct, as our simplified expression has a positive term before \$\sqrt(10)\$ |
\$3 - \sqrt(12)\$ |
10 |
Choice.D |
This option is not correct, as our simplified expression does not involve \$\sqrt(12)\$ |
\$3 + \sqrt(12)\$ |
11 |
Answer |
Option |
A |
12 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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