Question

Find \[3\sqrt 6 + 4\sqrt 6 \] is equal to?

Answer 1

Hint: Here the given question based on the addition of Radicals, we have to add the given two radicals. First, we should check the two radicals as like radicals, otherwise convert the two radicals as like radicals by using the square factors of the number and next by adding the coefficients of like radicals we get the required solution.

Complete step-by-step answer:
The square root of a natural number is a value, which can be written in the form of \[y = \sqrt a \]. It means ‘y’ is equal to the square root of a, where ‘a’ is any natural number. We can also express it as \[{y^2} = a\].Thus, it is concluded here that square root is a value which when multiplied by itself gives the original number, i.e., \[a = y \times y\].
The symbol or sign to represent a square root is ‘\[\sqrt {} \]’. This symbol is also called a radical. Also, the number under the root is called a radicand.
Consider the given expression:
\[ \Rightarrow 3\sqrt 6 + 4\sqrt 6 \]
To add or subtract radicals, we must have "like radicals" that is the radicands and the index must be the same for each term.
In the given expression, the radicands and index are the same in both terms, then two are like radicals.
Then add the like radicals by adding their coefficients:
\[ \Rightarrow \left( {3 + 4} \right)\sqrt 6 \]
\[ \Rightarrow 7\sqrt 6 \]
Hence, the required solution is \[7\sqrt 6 \].
So, the correct answer is “Option B”.

Note: The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\], where a is the numeral and n represents the number of times the number is multiplied. For the exponential numbers we have a law of indices and by applying it we can solve the given number. Remember when doing the addition and subtraction of exponential and radicand we have to make the like terms first.