Question

How do you multiply $\sqrt {98} \times 2\sqrt {50} $?

Answer 1

Hint: The given question is related to the concept of radicals. Here, in the given question, the radical is a square root. We have to multiply two radicals, in this case that are two square roots in order to obtain a natural number as our required solution. We will start solving this question by first multiplying the square roots and then, square root whatever number obtained and then multiplying it by $2$.

Complete step by step answer:
For solving this question, the concept of radical expressions must be clear to the students. Those expressions which contain the radical symbol $\sqrt[n]{{}}$ are known as radical expressions. The power is written just outside the radical symbol, taking the place of $n$ whereas the base is written inside the symbol. The power is represented in the form of $\dfrac{1}{n}$.

Given is $\sqrt {98} \times 2\sqrt {50} $. To start solving this question, we will first multiply the two radicals or the square roots i.e.,$\sqrt {98} $ and $\sqrt {50} $. Doing so, we get,
$\Rightarrow \sqrt {98} \times \sqrt {50} \\
\Rightarrow \sqrt {4900} \\ $
We know that the square root of $4900$ is
$ \Rightarrow \sqrt {4900} = 70$
Now, we multiply the obtained number that is, $70$ by $2$ and we get,
$\Rightarrow 70 \times 2 \\
\Rightarrow 140 \\ $
Therefore, $\sqrt {98} \times 2\sqrt {50} = 140$.

Hence, our required answer is $140$.

Note:A radical symbol $\sqrt {} $ is only used when we have to represent a radical expression but most of the time students misread it as a square root symbol. Though in the given case, it represented a square root only. Apart from square roots, this radical symbol can also be used to denote cube root, fourth root or higher roots whose numbers are written in their place accordingly.