Question

What is the square root of 2 times 5 square roots of 2?

Answer 1

Hint: We convert the given question from a word statement to a mathematical form and simplify the expression using basic mathematical techniques. We obtain the expression as $\sqrt{2}\times 5\sqrt{2}.$ We need to know the concept or square roots to simplify this expression. Using this concept, we obtain the final answer.

Complete step by step solution:
In order to solve this question, let us explain the concept of multiplying square roots. We know that when we multiply two square root terms, we get a product of the terms inside the square roots. This can be shown as follows,
$\Rightarrow \sqrt{a}\times \sqrt{b}=\sqrt{a\times b}$
Using this, let us solve the above question. First, we need to convert this from a word problem to a mathematical form. The mathematical representation of the question can be given as,
$\Rightarrow \sqrt{2}\times 5\sqrt{2}$
We simplify this by using the concept shown above by taking the product of the two root terms.
$\Rightarrow 5\sqrt{2\times 2}$
The terms can be multiplied inside the square root as shown,
$\Rightarrow 5\sqrt{4}$
We know the square root of 4 is nothing but $ 2$ . Using this, we get
$\Rightarrow 5\times 2$
Since none of the terms here involve a square root here, taking a product of these terms gives us,
$\Rightarrow 10$

Hence, the square root of 2 times 5 square roots of 2 is $ 10$

Note: We need to know the basic concepts of square roots in order to solve such questions. We can also solve this question by taking the 5 inside the square root as 25 since any term that is taken inside a square root will be a squared version of the original number. Then the term in the square root becomes 4 times 25 which is 100. Square root of 100 is given by $ 10$ which is the same as the answer obtained above.