Question

How do you solve \[\sqrt {3x - 6} = 0\] ?

Answer 1

Hint: In order to solve and write the expression into the simplest form . The square root is related to figuring out what should be the number which when multiplied by itself is equal to the number under the square root symbol $ \sqrt {} $ . This symbol is known as radical . Since in our case we have given the question in which we have to solve and find the value of x , we will first get rid of the radical and remove the square root as we want the original value of x , by somewhere using equivalent equations . Equivalent equations are said to be algebraic equations that may have the same solutions if we add or subtract the same number to both sides of an equation - Left hand side or Right hand side of the equal to sign . Or we can multiply or divide the same number to both sides of an equation - Left hand side or Right hand side of the equal sign . . After eliminating the radical , we will then solve the equation by simplifying further and find the value of the x .

Complete step-by-step answer:
If we see the question , we need to solve the given expression under the square root which is \[\sqrt {3x - 6} = 0\] . -----equation 1
By applying the concept of equivalent equation , we will first do squaring both sides on \[\sqrt {3x - 6} = 0\] both the L . H . S . and the R . H . S . as follows –
We are going to isolate a square root on the L . H . S . So that we can simplify as stated below –
\[\sqrt {3x - 6} = 0\]
\[{\left( {\sqrt {3x - 6} } \right)^2} = {(0)^2}\]
After squaring , we get –
 $ 3x - 6 = 0 $
Adding 6 to both the L . H . S . and the R . H . S . we get ,
 $ 3x = 6 $
Dividing by 3 to get the original value of x we get ,
 $
\Rightarrow x = \dfrac{6}{3} \\
\Rightarrow x = 2 \;
  $
Therefore , the required and final answer is $ x = 2 $ .
So, the correct answer is “ $ x = 2 $ ”.

Note: Always try to get rid of the square root .
We can use prime factorisation for the number inside the radical and pull out non- radical terms or perfect squares from the inside of the square root to make the solution easier .
: In equivalent equations which have identical solutions we can perform multiplication or division by the same non-zero number both L.H.S. and R.H.S. of an equation .
In an equivalent equation which has an identical solution we can raise the same odd power to both L.H.S. and R.H.S. of an equation .
Cross check the answer and always keep the final answer simplified .