Question

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

Answer 1

Hint: We will equate the given value to a variable $x.$ Then, we will square the whole equation. Later, we will try to find the square root of the value in the tenth and hundredth decimal places.

Complete step by step answer:
Consider the given value $\sqrt{0.16}$ which is the square root of a decimal number.
We are supposed to equate the given value to a variable, say $x.$
By this procedure, we will get $\sqrt{0.16}=x.$
Now we are going to square $x$ and so, we will square the given value, because they both are equal.
We will get ${{x}^{2}}=0.16.$
Now, let us consider the digits after the decimal point. We have $1$ in the tenth decimal place and $6$ in the hundredth decimal place.
Let us just keep the decimal point away.
So, we have the two digit number $16.$
Without any doubt we can say that $16$ is a perfect square.
And hence we will get $16=4\times 4={{4}^{2}}.$
Here, we have the number $0.16.$
That is, there are two decimal positions in the number. That means the root will be a number which has only one decimal position.
So, we will get $0.16=0.4\times 0.4={{0.4}^{2}}.$
We will get ${{x}^{2}}={{0.16}}={{0.4}^{2}}.$
So, we will get $x=\sqrt{{{0.4}^{2}}}.$
Now we know that the square root and the square act as inverse operations when they act together on a number.
Thus, we will get $x=0.4.$

Hence $\sqrt{0.16}=0.4.$

Note: We know that if we multiply two decimal numbers, then
First: we remove the decimal points of both the numbers.
Second: we multiply the whole numbers.
Third: we count the number of digits in the decimal positions of both the numbers.
Fourth: we count the digits of the product from the right side to see where we need to put the decimal point. The number of decimal positions in the product is equal to the sum of the number of decimal positions in both numbers to be multiplied.