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,
 $(a-b{)}^2=a^2+b^2-2ab$