Question

How do you simplify $ 10 $ square root $ 6 $ times square root $ 2 $ ?

Answer 1

Hint: For answering this question we need to write the given statement $ 10 $ square root $ 6 $ times square root $ 2 $ should be written mathematically as $ 10\sqrt{6}\times \sqrt{2} $ . It needs to be further simplified by performing simple arithmetic calculations.

Complete step by step answer:
Now considering the question we have to simplify the given statement mathematically.
The given statement is $ 10 $ square root $ 6 $ times square root $ 2 $ mathematically it can be given as $ 10\sqrt{6}\times \sqrt{2} $ .
This can be simplified by performing simple arithmetic calculations like multiplications.
Here initially we will multiply the two numbers under the root.
After that we will have $ 10\sqrt{6\times 2}=10\sqrt{12} $ .
The number $ 12 $ can be expressed as the product of $ 4 $ and $ 3 $ where $ 4 $ is a perfect square. So we can write it in reduced form as $ 10\times 2\times \sqrt{3} $ since the square root of $ 4 $ is $ 2 $ .
After performing the multiplication here we will have $ 20\sqrt{3} $.
Hence we can conclude that the simplified form of the given statement $ 10 $ square root $ 6 $ times square root $ 2 $ is given as $ 20\sqrt{3} $ .

Note:
 We should be sure with our calculations while performing this type of simple question. We should carefully convert the given statement in the form of mathematics. Similarly we can do many other simplifications like for the statement $ 5 $ square root $ 8 $ times square root $ 2 $ which can be mathematically written as $ 5\sqrt{8}\times \sqrt{2} $ which can be simplified as $ 5\sqrt{8\times 2}=5\sqrt{16}=5\left( 4 \right)=20 $ . This type of question can be performed simply but care should be taken while converting the statement mathematically.