How Do You Figure Out if a Square Root is Bigger than Another Number?

The line going over the 2 is the symbol for square root
We need to figure out what inequality symbol goes between the two numbers
Squaring both sides will undo the square root
The square root of 2 squared just equals 2
1.5² = 2.25
'<' means 'less than'
Since we didn't change the inequality when we squared both sides, we can use the same inequality symbol for our original problem

1. The inequality symbol will tell us which of the two numbers is bigger
1. We could find a decimal approximation with a calculator
2. Then we would be able to tell if it was bigger or smaller than 1.5
1. Comparing two decimals is a lot easier than comparing a square root and a decimal!
2. But there is another way we could find the answer without having to use a calculator
1. Squaring √2 will undo the square root
2. Squaring something just means we're raising it to the 2nd power
1. Remember, we need to square both of our numbers to preserve the inequality
1. Since squaring is the opposite of taking the square root, it gets rid of the square root
1. 1.5² = 2.25
1. Getting rid of the square root makes our numbers much easier to compare!
1. Now we need to determine what inequality sign goes in between the numbers
1. The inequality symbol we'll put in between our numbers is '<', because 2 is less than 2.25
1. Since we squared both of the numbers, the inequality didn't change
2. So whichever number was bigger before we squared them is still bigger
3. This means we can use the same inequality symbol we found here in our original problem
1. Since 2 < 2.25, √2 < 1.5

What is bigger, the square root of 2, or 1.5?