Question

How do you simplify `\sqrt{0.16}` without using a calculator?

Answer 1

This is actually an easy square root to solve, despite being a decimal. When seeing decimals, it can be kind of confusing because decimals, and fractions, have all of these special rules when adding and subtracting and doing all kinds of operations. When you square root 16:
`sqrt(16)`
The answer is 4.
It would make sense to square root 0.16 and get 0.04.

In fact, that is exactly what the answer is.

`sqrt(0.16) =0.4`

Seems easy enough.
So does this mean `sqrt(0.4)=0.2`?

NO

`sqrt(0.4)` is basically saying `sqrt(40/100)`

40 is not a perfect square, so the answer would be an irrational decimal number.

So what square root equals 0.2?
`sqrt(0.04)`

If a number takes up 2 decimal points to the hundredths place, multiply it by 100 and the result is a perfect square, you can use this rule to find the square root of decimals.

If the decimal is, say, 0.0144, you would have to multiply by 10,000 to get 144. so; `sqrt(0.0144)=0.12`.
and if the decimal is 1.44, you only have to multiply by 100, making the square root 1.2.

In summation, all you need to do is move the decimal two positions a certain amount of times until you get a perfect square. It is all just a moving of decimals two number places or any multiple of two.