Question

Use a square root table to answer the following question

V47 falls within what interval

A. 5.5 to 6
B. 6 yo 6.5
C. 6.5 to 7
D. 7 to 7.5

Determine if the number is rational or irrational

1. V84
2. Pi
3. V256

A. Irrational
B. Rational

Answer 1

To determine where \( \sqrt{47} \) falls, we can use a square root table or estimate the square roots of perfect squares close to 47.

The perfect squares close to 47 are:
- \( 6^2 = 36 \)
- \( 7^2 = 49 \)

Since \( 36 < 47 < 49 \), it follows that:
\[ 6 < \sqrt{47} < 7 \]

To refine further, we can also check:
- \( 6.5^2 = 42.25 \)
- \( 6.7^2 = 44.89 \)
- \( 6.8^2 = 46.24 \)
- \( 6.9^2 = 47.61 \)

Since \( 6.8^2 \) is approximately 46.24 and \( 6.9^2 \) is approximately 47.61, we can see that \( \sqrt{47} \) is between \( 6.8 \) and \( 6.9 \).

Therefore, \( \sqrt{47} \) falls into the interval:
**C. 6.5 to 7**

Next, we will determine if each given number is rational or irrational:

1. **\( \sqrt{84} \)**:
- \( 84 \) is not a perfect square, which means \( \sqrt{84} \) is an irrational number.
- Answer: **A. Irrational**

2. **\( \pi \)**:
- \( \pi \) is a well-known mathematical constant and is not expressible as a fraction of two integers, so it is irrational.
- Answer: **A. Irrational**

3. **\( \sqrt{256} \)**:
- \( 256 \) is a perfect square since \( 16^2 = 256 \), so \( \sqrt{256} = 16 \), which is rational.
- Answer: **B. Rational**

In summary:
- \( \sqrt{47} \) falls within **C. 6.5 to 7**.
- \( \sqrt{84} \): **A. Irrational**
- \( \pi \): **A. Irrational**
- \( \sqrt{256} \): **B. Rational**