How do you simplify the square root of \[35\] times square root of 10?

Hint: We can simplify the above question by remembering the basic fact about square root which is that they cannot be added with each other but can easily be multiplied with each other and will result in the square root of the number which is formed by the multiplication of the two numbers and after getting that square root we can easily evaluate by factoring the number into perfect squares if possible and letting remaining part remain under the square root sign.

Complete step by step solution:
We are given the expression, say \[A\] , as
 \[A = \sqrt {35} \times\sqrt {10} \]
Now since we know that square root can be multiplied easily but not added but since we are given to find the multiplication we can easily multiply them, so multiplying the two numbers and putting them both under square root sign we get,
 \[A = \sqrt {350} \]
Now since we have to simplify if further we will now try to express 350 in the factors of perfect squares and letting remaining part remain under the square root sign, thus writing the expression as,
 \[A = \sqrt {5\times5\times7\times2} \]
Now only $5$will go out of square root sign \[7\times2\] will remain inside the square root sign, thus we write as,
 \[A = 5\sqrt {7\times2} \] , thus final answer is written as,
 \[A = 5\sqrt {14} \] which is the required solution of the question.
So, the correct answer is “ \[A = 5\sqrt {14} \] ”.

Note: The different square roots cannot be added to each other but they can be easily multiplied to each other and can then later be factorized easily.