Approximating irrational number exercise example | Pre-Algebra | Khan Academy

TL;DR

The video explains how to estimate the square root of 43 using a number line and approximation, with point A being a closer approximation than point B.

Transcript

On the number line below, which point more closely represents the principal root of 43? Or you could view it as the positive square root of 43. And I encourage you to pause this video and, just looking at this, try to approximate where A is and where B is. And let's think about which of those numbers is closer to the principal root of 43. So let's ... Read More

Key Insights

• 🫥 The video explains how to use a number line to estimate the square root of 43 without a calculator.
• 😚 Point A, around 6.56 on the number line, is determined to be a close approximation to the square root of 43.
• 😥 Squaring the estimated value of point A confirms that it is already greater than 43.
• ❓ Applying approximation techniques can be useful in situations where calculator usage is not desired or available.
• 🫚 The method showcased in the video can be used to estimate square roots of other numbers as well.
• 🫥 The estimation process involves visualizing the number line and approximating a point between two values.
• 😥 Point B is ruled out as an approximation due to point A's already greater squared value.

Questions & Answers

Q: How is the square root of 43 approximated in the video?

The square root of 43 is approximated by locating point A, around 6.56 on the number line, and squaring it without using a calculator.

Q: Why is point A considered a better approximation than point B?

Point A is considered a better approximation as its squared value, 43.0336, is already greater than 43, indicating it is slightly larger than the square root of 43.

Q: What is the purpose of this exercise?

The purpose of the exercise is to demonstrate an approximation method for estimating the square root of 43 without relying on a calculator.

Q: How does ruling out point B save computation?

Ruling out point B saves computation as squaring point B would have resulted in a value even further above 43 than point A, making it unnecessary to calculate.

Summary & Key Takeaways

• The video demonstrates how to estimate the square root of 43 without using a calculator by approximating on a number line.

• Point A, located around 6.56 on the number line, is estimated to be closer to the principal root of 43 than point B.

• Squaring the approximate value of point A confirms that it is already greater than 43, ruling out point B.