Question

Can the square root of $10$ be simplified?

Answer 1

Hint: In this question we have to check whether the square root of $10$ be simplified or not. It can be written as $\sqrt {10} $ . We will break down the number in the multiplication of factors and then we will check whether it can be further simplified or not.
We know that the square root of the number $'x'$ is the number $'y'$, So it can be written as ${y^2} = x$ .

Complete step-by-step answer:
In this question we have $\sqrt {10} $ .
We will break down the number into its factors i.e.
$\Rightarrow10 = 5 \times 2$
So by putting the value in the expression we have
$\Rightarrow \sqrt {5 \times 2} $ .
We will apply the formula:
$\Rightarrow \sqrt {a \times b} = \sqrt a \cdot \sqrt b $ .
By comparing from the formula we get
$a = 5,b = 2$
So by applying the formula we get
$\Rightarrow \sqrt {5 \times 2} = \sqrt 5 \cdot \sqrt 2 $ .
However we can see that there are no perfect square factors, so this is the last simplified value we can get.
Hence $\sqrt {10} $ can be written as $\sqrt 5 \cdot \sqrt 2 $
So, the correct answer is “$\sqrt 5 \cdot \sqrt 2 $ ”.

Note: We should know the formula of multiplication and division radicals. The formula of division radical is
$\sqrt {\dfrac{a}{b}} = \dfrac{{\sqrt a }}{{\sqrt b }}$ .
We know that when we have a square root in the denominator of an expression, we can remove it by rationalising the value i.e. by multiplying and dividing the fraction with the same quantity as the denominator.
As for example, let us take value
$\dfrac{3}{{\sqrt 2 }}$ .
Now we can remove the denominator by multiplying and dividing with $\sqrt 2 $ i.e.
 $\dfrac{3}{{\sqrt 2 }} \times \dfrac{{\sqrt 2 }}{{\sqrt 2 }}$ .