Question

How do you simplify \[\sqrt{12{{x}^{2}}}\]?

Answer 1

Hint: For the given solution we are given that to solve the problem\[\sqrt{12{{x}^{2}}}\]. Now we have to assume the number as ‘A’ and then by using the exponent formulas solve the square root of \[12{{x}^{2}}\]. Therefore that will be the result.

Complete step by step solution:
Let us consider the given equation as equation (1) and assume it as ‘A’.
\[A=\sqrt{12{{x}^{2}}}...................\left( 1 \right)\]
First of all we have to rewrite \[\sqrt{12{{x}^{2}}}\]as multiplication of perfect square and some constant.
Therefore let us write \[12{{x}^{2}}\]as \[4{{x}^{2}}\cdot 3\], we get
\[\Rightarrow 12{{x}^{2}}=4{{x}^{2}}\cdot 3\]
Now we have to rewrite the equation by substituting above formation, we get
\[\Rightarrow A=\sqrt{4(3){{x}^{2}}}\]
Let us consider the above equation as equation (2), we get
\[\Rightarrow A=\sqrt{4(3){{x}^{2}}}..........\left( 2 \right)\]
Now we should rewrite 4 as \[{{2}^{2}}\]in the equation (2), we get
\[\Rightarrow A=\sqrt{{{2}^{2}}(3){{x}^{2}}}\]
\[\Rightarrow A=\sqrt{{{2}^{2}}{{x}^{2}}\cdot 3}\]
\[\Rightarrow A=\sqrt{{{\left( 2x \right)}^{2}}\cdot 3}\]
Let us consider the above equation as equation (3), we get
\[\Rightarrow A=\sqrt{{{\left( 2x \right)}^{2}}\cdot 3}..........\left( 3 \right)\]
Now by using the formula \[\sqrt{x.y}=\sqrt{x}.\sqrt{y}\], we will get the equation (3) as
\[\Rightarrow A=\sqrt{{{\left( 2x \right)}^{2}}}.\sqrt{3}\]
Let us consider the above equation as equation (4), we get
\[\Rightarrow A=\sqrt{{{\left( 2x \right)}^{2}}}.\sqrt{3}........\left( 4 \right)\]
Now after cancelling all the roots in the equation (4), we get the solution as
\[\Rightarrow A=2x\cdot \sqrt{3}\]
Let us consider the above equation as equation (5), we get
\[\Rightarrow A=2x\cdot \sqrt{3}.......\left( 5 \right)\]
Therefore, the equation (5) is the exact one for the given problem.

Note: While doing this problem we should be aware of the perfect square which means a number which gives a whole number if we find the root of the number. We should remember that \[x=\sqrt{x}.\sqrt{x}\]. We should note a point that if we have to find the root for a perfect square then we have to convert the number as multiplication of a perfect square and a constant.