What is the simplified value of [(1/√3) (√(t – 5))]²?


To simplify the expression \(\left[\frac{1}{\sqrt{3}} \cdot \sqrt{t - 5}\right]^2\), let's follow the steps:

### Step 1: Apply the square to both terms inside the parentheses.
We can distribute the square over the product:
\[
\left[\frac{1}{\sqrt{3}} \cdot \sqrt{t - 5}\right]^2 = \left(\frac{1}{\sqrt{3}}\right)^2 \cdot \left(\sqrt{t - 5}\right)^2
\]

### Step 2: Simplify each squared term.
- \(\left(\frac{1}{\sqrt{3}}\right)^2 = \frac{1}{3}\)
- \(\left(\sqrt{t - 5}\right)^2 = t - 5\)

### Step 3: Combine the results.
Multiplying the two simplified terms gives:
\[
\frac{1}{3} \cdot (t - 5) = \frac{t - 5}{3}
\]

So, the simplified value is:
\[
\frac{t - 5}{3}
\]

Would you like further clarification or additional details on any step?

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Here are 5 related questions to explore:
1. What is the simplified form of \(\left(\frac{1}{\sqrt{x}} \cdot \sqrt{y}\right)^2\)?
2. How would you differentiate \(\frac{t - 5}{3}\) with respect to \(t\)?
3. Can you simplify \(\left[\frac{2}{\sqrt{5}} \cdot \sqrt{x + 1}\right]^2\)?
4. How do you rationalize the denominator of \(\frac{1}{\sqrt{3}}\)?
5. What is the square of \(\left(\frac{a}{\sqrt{b}}\right)\)?

**Tip:** When squaring a product, square each term separately, and then multiply the results.

What is the simplified value of [(1/√3) (√(t – 5))]²?

Discover how to simplify the expression [(1/√3) (√(t – 5))]² step by step. This solution demonstrates key algebraic concepts such as exponentiation and square roots. Suitable for students in Grades 9-10.

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