# How To Find The Square Root of Large Numbers Mentally | Summary and Q&A

957.7K views
January 23, 2020
by
The Organic Chemistry Tutor
How To Find The Square Root of Large Numbers Mentally

## TL;DR

Learn how to find the square root of a perfect square, with examples and patterns for different digits.

## Key Insights

• ❎ Patterns of perfect squares can help determine the unit digit of the square root.
• 🟧 Comparing the number to the squares of whole numbers helps narrow down the range of possible square roots.
• 🟧 Deciding between two possible square roots depends on which range the number is closer to.
• 💯 These methods are only applicable to perfect squares, not non-perfect squares.

## Transcript

consider this problem what is the square root of 1156 given that you know the answer is an integer or a whole number how would you find the answer well in this video we're going to talk about how to do just that but first we need to talk about the patterns of perfect squares so i'm going to write down a few as i write these down notice what you see... Read More

### Q: How can patterns of perfect squares help find the square root of a large number?

By observing the patterns, we can deduce that the last digit of the square root will match the last digit of the perfect square.

For example, if the last digit is 4 or 6, the square root will have a last digit of 2 or 8, respectively. This narrows down the possibilities.

### Q: When finding the square root of a number, how do you determine the first digit?

Compare the number to the square of whole numbers to find the range of possible square roots. Pick the lower number as the first digit.

For example, if the number is between the square of 3 and 4, the first digit will be 3.

### Q: How do you choose between two possible square roots?

Consider which range the number is closer to. If it is closer to the higher range, choose the higher square root. If it is closer to the lower range, choose the lower square root.

### Q: Can these patterns be used to find the square root of non-perfect squares?

No, these patterns only apply to perfect squares. When dealing with non-perfect squares, approximation or other methods are needed to find the square root.

## Summary & Key Takeaways

• The video discusses the patterns of perfect squares and how they can be used to find the square root of a number.

• Perfect squares ending in 1 or 9 have a unit digit of 1.

• Perfect squares ending in 2 or 8 have a unit digit of 4.

• Perfect squares ending in 3 or 7 have a unit digit of 9.

• Perfect squares ending in 4 or 6 have a unit digit of 6.

• Perfect squares ending in 5 have a unit digit of 5.

• Perfect squares ending in 0 have a unit digit of 0.