Question

How do you simplify $\sqrt{1.6}$?

Answer 1

Hint: To solve these types of questions we should be able to convert the decimal into a fraction and then do factorization to get the possible pairs which can get further simplified.

Complete step by step solution:
First of all, it is given in the question that we need to simplify $\sqrt{1.6}$,
As we know we can convert a decimal into a fraction by simply multiplying $10$ to both the numerator and the denominator,
Hence, $\sqrt{1.6}=\sqrt{{\displaystyle \frac{16}{10}}}$
$\sqrt{{\displaystyle \frac{2\times 2\times 2\times 2}{2\times 5}}}$$\Rightarrow \sqrt{{\displaystyle \frac{2\times 2\times 2\times 2}{2\times 5}}}$
Now we will after cutting out the common terms we get,
$\Rightarrow \sqrt{{\displaystyle \frac{2\times 2\times 2}{5}}}$
As we know we have $1$ pair of $2$, we will take it out and the equation will become,
$\Rightarrow 2\sqrt{{\displaystyle \frac{2}{5}}}$
Now, on multiplying $\sqrt{5}$ on both the numerator and denominator we get,
$\Rightarrow {\displaystyle \frac{2}{5}}\sqrt{10}$

Hence, the simplest form of $\sqrt{1.6}$ can be written as ${\displaystyle \frac{2}{5}}\sqrt{10}$.

Note:
A decimal is simply a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point.
Factorization consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.