Question

How do you simplify $\sqrt{8}.\sqrt{10}$?

Answer 1

Hint: To solve the given expression first we write the given numbers in the form of factors. As the given numbers are not perfect squares so we will factorize the numbers and write them into exponential form. Then by simplifying the obtained equation we will get the desired answer.

Complete step by step answer:
We have been given an expression $\sqrt{8}.\sqrt{10}$.
We have to solve the given expression.
Now, first we will write the factors of 8 and 10. Then we will get
$\Rightarrow 8=2\times 2\times 2$ and $\Rightarrow 10=2\times 5$
Now, substituting the values we will get
$\Rightarrow \sqrt{2\times 2\times 2}.\sqrt{2\times 5}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \sqrt{{{2}^{2}}\times 2}.\sqrt{2\times 5}$
Now, we know that $\sqrt{a}.\sqrt{b}=\sqrt{a.b}$
So applying the property we will get
\[\Rightarrow \sqrt{{{2}^{2}}}.\sqrt{2}.\sqrt{2}.\sqrt{5}\]
Now, we know that square root and square cancel each other then we will get
\[\Rightarrow 2.\sqrt{2}.\sqrt{2}.\sqrt{5}\]
Now, further simplifying the above obtained equation we will get
\[\Rightarrow 2\times 2\sqrt{5}\]
Now, further simplifying the above obtained equation we will get
$\Rightarrow 4\sqrt{5}$
Hence above is the required simplified form of the given expression.

Note:
Alternatively students may solve the given expression by using the square root property $\sqrt{a}.\sqrt{b}=\sqrt{a.b}$.
Now, applying the property to the given expression we will get
$\Rightarrow \sqrt{8\times 10}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \sqrt{80}$
Now, let us find the square root of 80 by using the prime factorization method we will get
\[80=2\times 2\times 2\times 2\times 5\]
Now, we can group the factors into pair of two we will get
$\Rightarrow \sqrt{80}=4.\sqrt{5}$