Lesson Example Discussion Quiz: Class Homework |
Step-2 |
Title: Equivalent expressions |
Grade: 1400-a Lesson: S1-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Simplify the expression \$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$. |
|
2 |
Step |
The given expression is |
\$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ |
3 |
Step |
Start with the expression |
\$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ |
4 |
Clue |
First, let’s simplify the individual square roots within each radical term |
\$ \sqrt(a+b) = \sqrt(a) + \sqrt(b) \$ \$ \sqrt(a-b) = \sqrt(a) - \sqrt(b) \$ |
5 |
Step |
Now let’s apply these simplification rules to our expression |
\$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ = \$ \sqrt((\sqrt(5))^2 + (\sqrt(2\sqrt(6)))^2) \$ + \$ \sqrt((\sqrt(5))^2 - (\sqrt(2\sqrt(6)))^2) \$ |
6 |
Step |
Make it simplify |
\$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ = \$ \sqrt5 + \cancel(2\sqrt(6)) + \sqrt5 - \cancel(2\sqrt(6) )\$ |
7 |
Step |
After simplification |
\$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ = \$ \sqrt5 + \sqrt5 \$ \$\sqrt(5 + 2\sqrt6) + \sqrt(5 - 2\sqrt6)\$ = \$ 2\sqrt5 \$ \$ 2\sqrt5 \$ |
8 |
Step |
Therefore, the simplified expression is \$ 2\sqrt5 \$. |
|
9 |
Choice.A |
\$10\sqrt(5)\$, is incorrect because it’s not possible to simplify the expression to \$\sqrt(5)\$ without any other term |
\$ 10\sqrt5 \$ |
10 |
Choice.B |
Incorrect: It incorrectly assumes that both terms are \$\sqrt(6)\$, which is not the case |
\$ 3sqrt6 \$ |
11 |
Choice.C |
Correctly calculated using hint and clue, it was done with precision and accuracy |
\$ 2\sqrt5 \$ |
12 |
Choice.D |
Wrong: Because the expression does not yield a negative result |
\$ -2\sqrt5 \$ |
13 |
Answer |
Option |
C |
14 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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