Question

What is the square root of $1.8$?

Answer 1

In the given question, we need to find the square root of $1.8$ so we are asked to find the value of $\sqrt {1.8}$. We can find the square root of decimals by converting it into rational numbers. We can easily find this using a calculator but we are going to see a method to find the square root of any number.

Complete step by step answer:
Solving the square root of$1.8$, i.e. $\sqrt {1.8}$
To find the square root of this decimal we convert it into a fraction part first.
$1.8 = \dfrac{9}{5}$ $1.8 = \dfrac{9}{5}$
Square root the fraction
$= \sqrt {\dfrac{9}{5}}$
Take out the perfect square
$= \dfrac{3}{{\sqrt 5 }}$
Now rationalizing the denominator
$= \dfrac{3}{{\sqrt 5 }} \times \dfrac{{\sqrt 5 }}{{\sqrt 5 }}$
$= \dfrac{{3 \times \sqrt 5 }}{{\sqrt {5 \times \sqrt 5 } }}$
Further,
$= \dfrac{{3\sqrt 5 }}{5}$
Put the value of$\sqrt 5$
$= \dfrac{{3 \times 2.23606798}}{5}$
$= \dfrac{{6.70820394}}{5}$
By Solving, we get
$= 1.34164079$
Therefore the square root of the $1.8$ is $1.34164079$

Note:
The $\sqrt {}$ symbol is called the radical sign. To simplify the square root of $1.8$ means to find the simplest radical form of $\sqrt {1.8}$. Calculating square roots is easy if you have a perfect square. If you don't, there's a logical process you can follow to systematically figure out the square root of any number, even if you don’t use a calculator. The given number in this question is not a perfect square hence it is not going to have an exact answer. You can also find the square root of any number using the long division method.