Question

State whether the following equation is True or False.
\[\sqrt 2 + \sqrt 3 = \sqrt 5 \]
A) True
B) False

Answer 1

Hint: Find separate under root values for each of the numbers and add the numbers on L.H.S and R.H.S. respectively,and equate L.H.S. to R.H.S. then you can able to find the final answer easily.

Complete step by step solution:
Step 1:
Firstly we need to understand hint clearly to for finding the solution easily,hint is the major key factor to solve a question easily in very much approachable method
Keeping the hint in our mind,firstly we need to find under-root values of each number which are mentioned in the question
So the values of \[\sqrt 2 ,\sqrt 3 ,\sqrt 5 \] are
\[
  \sqrt 2 = 1.414, \\
  \sqrt 3 = 1.732, \\
  \sqrt 5 = 2.236. \\
 \]
Substitute the values in the given question,in order to find the final answer of the given question
Step 2:
Substitute the values of L.H.S. under root values in their position
,and substitute the R.H.S. under root values in their respective position
i.e, substitute
\[
  \sqrt 2 = 1.414, \\
  \sqrt 3 = 1.732, \\
  \sqrt 5 = 2.236. \\
 \]
In the equation \[\sqrt 2 + \sqrt 3 = \sqrt 5 \]………(1)
Step 3:
Now rewrite equation (1) as L.H.S. and R.H.S. values separately by substituting their respective values
L.H.S. \[ = \sqrt 2 + \sqrt 3 = 1.414 + 1.732 = 3.146\]
Similarly,R.H.S. \[ = \sqrt 5 = 2.236\]
This shows that L.H.S. not equal to R.H.S.
Therefore, option (B) is correct.

Note:
We can't add the under root values directly same like the addition of normal integers,but we can add them directly by replacing with their respective values
Alternative method :
Consider L.H.S and R.H.S. separately and square them respectively,
Thereafter consider the v
Final square values of L.H.S. and R.H.S
i.e, the square value of L.H.S. is
\[{(\sqrt 2 + \sqrt 3 )^2} = 2 + 3 + 2\sqrt 6 = 5 + 2\sqrt 6 \]
Similarly,the square value of the R.H.S. is
\[{(\sqrt 5 )^2} = 5\]
This also clearly shows that L.H.S. not equal to R.H.S