Question

What is the square root of 12 times the square root of 3 ?

Answer 1

Hint:From the given question we have been asked to find the square root of \[12\] times the square root of \[3\]. We will write the Mathematical counterparts of each of the words given in the statement. We know that the word times implies the mathematical operation multiplication. The phrase 'square root of a number' is expressed as the number under the radical sign.

Complete step by step solution:
Let us consider the given statement 'square root of \[12\] times the square root of \[3\]'.
We need to find the operation in the given statement.
Let us consider the word 'times' in the statement. This word stands for when the operation takes place.
We know that a number times another number implies their product.
So, \[a\] times \[b\] implies the product of \[a\] and \[b\].
That is, \[ab\].
From this, we can learn that the given statement includes the operation multiplication. So, we can understand what we are discussing is the square root of \[12\] times the square root of \[3\].
We know that the square root of a number can be expressed as the number inside the radical sign. We usually express the square root of a number \[a\] as \[\sqrt{a}\].
Therefore, we can write the square root of \[3\] as \[\sqrt{3}\] and the square root of \[12\] as \[\sqrt{12}\] simply \[2\sqrt{3}\].
So, the given statement will become \[\sqrt{3}\times 2\sqrt{3}\].
We know that we can ignore the symbol while writing if the operation is multiplication.
So, the statement can be written as \[2\times 3=6\].
Therefore, the answer is \[2\times 3=6\].

Note: students should make calculation mistakes. Students should not confuse between square and square root of a number. When we multiply a number to itself, we get the square of that number. So, the square root of a number is a number which gives the former when multiplied to itself. That is, if \[a\times a={{a}^{2}}\], then \[{{a}^{2}}\] is called the square of \[a\] and \[a\] is called the square root of \[{{a}^{2}}\].