Question

Is \[\sqrt 5 + \sqrt 5 = \sqrt {10} ?\]

Answer 1

Hint: There is no hint particularly for this question. It is the general mathematics we have learnt. As the first two radicals are the same we will add them but that addition is not the addition of the number inside the radical. Thus the statement above or the simplification above is wrong.

Complete step by step solution:
Given that or rather it is asked that, \[\sqrt 5 + \sqrt 5 = \sqrt {10} ?\]
Now see \[\sqrt a + \sqrt a = 2\sqrt a \]
What it tells is when the same radicals are added we actually add their coefficients and not the radicals.
So, \[\sqrt 5 + \sqrt 5 = 2\sqrt 5 \]
This will be the process.
Rather, \[\sqrt {10} = \sqrt {2 \times 5} \] this can be expressed as a product of prime numbers. But that won't be written as \[2\sqrt 5 \].
Thus, \[\sqrt 5 + \sqrt 5 \ne \sqrt {10} \]
So, the correct answer is “, \[\sqrt 5 + \sqrt 5 \ne \sqrt {10} \]”.

Note: Take note that, radical is one of the symbols of mathematics. But we have some rules to be followed while operating on them. Like say the product of radicals is different and addition and subtraction is different.
\[\sqrt a .\sqrt a \ne 2\sqrt a \] the product of same radicals will change the power also.
\[\sqrt a .\sqrt a = a\] since the radical power is half. Two half make 1 complete. And power can be shown by blank also.