Approximating square roots to hundredths | Pre-Algebra | Khan Academy

TL;DR

The video explains how to approximate the square root of 45 without using a calculator, finding that it is approximately 6.71.

Transcript

We are asked to approximate the principal root, or the positive square root of 45, to the hundredths place. And I'm assuming they don't want us to use a calculator. Because that would be too easy. So, let's see if we can approximate this just with our pen and paper right over here. So the square root of 45, or the principal root of 45. 45 is not a ... Read More

Key Insights

• 🫚 The square root of 45 falls between the square roots of 36 and 49.
• 💯 By comparing the differences between these perfect squares, the position of 45 between them can be estimated.
• ❎ The initial guess of 6.7 is improved to 6.71 by calculating the square and comparing it to 45.

Questions & Answers

Q: How is the square root of 45 approximated without a calculator?

To approximate, the video suggests looking at nearby perfect squares and measuring the difference between them. By estimating the position of 45 between 36 and 49, an initial guess of 6.7 is made.

Q: How is the accuracy of the approximation improved from 6.7 to 6.71?

The square of the initial guess, 6.7, is calculated to be 44.89 which is 0.11 away from 45. By recalculating with 6.71, the square becomes 45.0241, narrowing the difference to just 0.0241.

Q: Why is it necessary to approximate the square root of 45?

Approximation techniques are useful when finding square roots without a calculator. In situations where only a rough estimate is required, it helps to have a method to quickly find a close value.

Q: Is the approximation of 6.71 the exact square root of 45?

No, the value of 6.71 is an approximation to the hundredths place and is not the exact square root of 45. It is simply a good estimate obtained using the given method.

Summary & Key Takeaways

• The square root of 45 is not a perfect square and falls between the square roots of 36 and 49.

• By measuring the difference between 36 and 49, it is estimated that the square root of 45 is approximately 0.69 of the way between 6 and 7.

• Using the initial guess of 6.7, the square is calculated to be 44.89. Adjusting the guess to 6.71 yields a square of 45.0241, indicating that 6.71 is a better approximation.