https://file.aiquickdraw.com/mathbot/file/1726164093166oof3xb6h.jpg

This worksheet asks to approximate the square root of 78 using perfect squares.

1. First, note that \( 78 \) is between two perfect squares: 
   \[
   64 \quad \text{and} \quad 81 \quad \text{(since} \ 64 = 8^2 \ \text{and} \ 81 = 9^2\text{)}.
   \]
   Therefore, \( 64 < 78 < 81 \).

2. Since \( 64 < 78 < 81 \), the square root of 78 lies between \( \sqrt{64} \) and \( \sqrt{81} \), which simplifies to:
   \[
   8 < \sqrt{78} < 9.
   \]

The conclusion is:
\[
\sqrt{78} \ \text{is between} \ 8 \ \text{and} \ 9.
\]

Would you like a more detailed explanation or additional assistance on this?

Here are 5 related questions to further explore this topic:
1. How can you estimate \( \sqrt{78} \) more precisely using interpolation?
2. What is the decimal approximation of \( \sqrt{78} \)?
3. How do you determine the square roots of non-perfect squares?
4. Why does \( \sqrt{78} \) fall between 8 and 9 specifically?
5. How can you find the square root of any number using long division?

**Tip**: To improve your estimation of square roots, consider using decimal approximations and methods like interpolation between perfect squares.

Approximate using perfect squares. What is the square root of 78?

Learn how to approximate √78 by identifying two perfect squares that it falls between. This worksheet guides students through number sense, square roots, and estimation skills. Perfect for middle school students (Grades 6-8).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation