Question

What is the answer of $ 2\sqrt 3 $ whole square?

Answer 1

Hint: The whole square of a number means that we have to calculate the square of all the numbers given in the radical form . The square of a radical is equal to the number under the radical without the root sign, when we will do the whole square of a number. Also when doing the square root of a number we should keep in mind that,
 $ {(a.b)^2} = {a^2}{b^2} $
Thus using this relation we will put the square on both the terms given in the radical form.

Complete step-by-step answer:
We have to do the whole square of the number
$ 2\sqrt 3 $
Since the number is made up of multiplication of two numbers, they are,
$ 2 $ and $ \sqrt 3 $ ,
We will use
$ {(a.b)^2} = {a^2}{b^2} $
The whole square of the number will thus be written as,
$ {(2\sqrt 3 )^2} = {2^2} \times {(\sqrt 3 )^2} $
We know that when a number under the root sign is square root is squared it means that the root sign of the number will be removed.
 $ {(\sqrt 3 )^2} = 3 $
So we can now write,
 $ {(2\sqrt 3 )^2} = {2^2} \times 3 $
The square of $ 2 $ is $ 4 $
Thus our expression becomes,
 $ {(2\sqrt 3 )^2} = 4 \times 3 $
Solving which we get as,
 $ {(2\sqrt 3 )^2} = 12 $
Therefore $ 12 $ is the final answer to the question.
So, the correct answer is “ 12”.

Note: We used the relation
 $ {(a.b)^2} = {a^2}{b^2} $
When we had to find the whole square of the number or the expression when the numbers are multiplied with each other for example in this case $ 2 $ and $ \sqrt 3 $ . But we will not use this relation when the numbers are in the addition or the subtraction, so in case we have to find the whole square of the number
 $ a + b $ instead of the above relation we will use .
 $ {(a + b)^2} = {a^2} + {b^2} + 2ab $
And if the expression in case is a difference of the two numbers we can write as,
 $ {(a - b)^2} = {a^2} + {b^2} - 2ab $