Question

Evaluate $\sqrt {1.69} $

Answer 1

Hint: For finding the square root of this number firstly we will remove the decimal then the number will be in fraction. The next step will be to reduce the number in such a way that it becomes the perfect square. And then we can easily solve it by putting the value. And in this way, we are going to solve it.

Complete answer:
So we have to find the square root of $1.69$ . First of all, we will remove the decimal. Since there are two digits after the point so there will be two zero in the denominator after removing the decimal. So the number will become,
$ \Rightarrow \sqrt {\dfrac{{169}}{{100}}} $
Now we know that the square of $13$ is equal to $169$ and the square of $10$ is a hundred. So the above fraction will be written as
$ \Rightarrow \sqrt {\dfrac{{{{13}^2}}}{{{{10}^2}}}} $
Since the numerator and the denominator both have the same power. Therefore, it can be written as
$ \Rightarrow \sqrt {{{\left( {\dfrac{{13}}{{10}}} \right)}^2}} $
And the square root will be canceled by the square, so we get the fraction as
$ \Rightarrow \dfrac{{13}}{{10}}$
And on dividing the numerator from the denominator, we get
$ \Rightarrow 1.3$

Therefore, the square root of $\sqrt {1.69} $ is $1.3$.

Note: Square root of a number is the number which when increased by itself gives the number whose square root is to be resolved as an answer. Finding the square root of a number is identical to raising a similar number to the power $\dfrac{1}{2}$. The square root of a number $x$ can be along these lines be written in remarkable structure as $x$. So this is the basic about the square root which we should keep in mind.