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

Question

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

Vedantu Content Team · Accepted Answer

Hint: The whole square of a number means that we have to calculate the square of all the numbers given in the radical form                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              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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 $

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