Question

Find the value of $\sqrt {12} \times \sqrt 8 $?

Answer 1

Hint: The above question is based on the concept of square root of a number. The main approach towards solving the equation is to reduce the number $\sqrt {12} $ and $\sqrt 8 $ into its factors and then further taking common terms and then multiplying both of them and get the result.

Complete step-by-step solution:
Square root of a number is a number which is multiplied by itself to give the original number. Now
suppose for example if a is the square root of b and it is represented as \[a = \sqrt b \] and also it can be
written as \[{a^2} = b\].Here the square root sign is called a radical sign. For example, the square of 2 is 4,
therefore, the square root of 4 is 2.
The above given expression is $\sqrt {12} \times \sqrt 8 $.
So first we will reduce the number 12 into its factors. Factors of 12 can be
\[12 = 2 \times 2 \times 3\]
So, on applying square root the common terms are taken outside the root we get,
\[\sqrt {12} = 2\sqrt 3 \]
Now we will reduce the number 8 into its factors. Factors of 8 can be
\[8 = 2 \times 2 \times 2\]
So, on applying square root the pair of common terms are taken outside the root we get,
\[\sqrt 8 = 2\sqrt 2 \]
Therefore, on multiplying it we get,
\[\sqrt {12} \times \sqrt 8 = 2\sqrt 2 \times 2\sqrt 3 = 4\sqrt 6 \]
So, by multiplying square roots we get the above value.

Hence the correct answer is $4\sqrt 6$

Note: An important thing to note is that the value is the root form it can further be simplified by writing it in decimal form. The value of \[\sqrt 6 \] is $2.449$ so on further multiplying the value of $2.449$ with the number 4 we get the decimal value as $9.79$.