Question

How do you simplify $\sqrt{7}.\sqrt{14}$?

Answer 1

Hint: First we will convert the given expression in mathematical form by applying the square root to both numbers. The given expression has brackets. It means we have to multiply the square roots of both the numbers as $\sqrt{7}.\sqrt{14}$.

Complete step by step solution:
We have been given an expression $\sqrt{7}.\sqrt{14}$.
We have to simplify the given expression.
Let us first convert the given expression into mathematical form. Then we will get
$\Rightarrow \sqrt{7}.\sqrt{14}$
Now, we know that we can write 14 in the form of factors as
$\Rightarrow 14=7\times 2$
Now, substituting the values we will get
$\Rightarrow \sqrt{7}.\sqrt{7\times 2}$
Now, we know that by square root property \[\sqrt{a\times b}=\sqrt{a}.\sqrt{b}\]
Now, by applying the property we will get
$\Rightarrow \sqrt{7}.\sqrt{7}.\sqrt{2}$
Now, we know that $\sqrt{a}.\sqrt{a}=a$
Now, substituting the value we will get
\[\Rightarrow 7\sqrt{2}\]
Hence on simplifying the given expression we get the value as $7\sqrt{2}$.

Note:
Students may further simplify the obtained value by substituting the value of $\sqrt{2}$. As the value of $\sqrt{2}$ is used in mathematics so students must remember the value. $\sqrt{2}$ is an irrational number and we can’t express it as a fraction. The value of $\sqrt{2}$ is $1.414$. It has an infinite number of decimals.
Now, substituting the value of $\sqrt{2}$ in the obtained solution we will get
$\Rightarrow 7\times 1.414$
Now, simplifying the above obtained equation we will get
$\Rightarrow 9.898$
Hence above is the simplified value of the given expression.