Question

What is the square root of \[12\] plus the square root of \[27\] ?

Answer 1

Hint: In this question, we need to find the value of the square root of \[12\] plus the square root of \[27\] . That is, we need to find the sum of the square root of \[12\] and the square root of \[27\] .The sum of two numbers is nothing but adding the two given numbers. Mathematically, the addition of two numbers is the method of calculating the two given numbers to know the sum of the given numbers. Here we need to add the given square roots . Mathematically, sum is signed by the plus symbol \[+\] and the symbol \[\sqrt{}\] is used to represent the square root. We need to factorise both the given numbers in the square root since both are not the perfect square numbers . After factoring the numbers, we can find the sum of the numbers.
Formula used :
\[a\sqrt{m} + b\sqrt{m} = \left( a + b \right)\sqrt{m}\]

Complete step-by-step solution:
Here we need to find the sum of the square root of \[12\] and the square root of \[27\] .
Notation :
The square root of \[12\] ,
\[\Rightarrow \ \sqrt{12}\]
The square root of \[27\] ,
\[\Rightarrow \ \sqrt{27}\]
Here both \[\sqrt{12}\] and \[\sqrt{27}\] is not a perfect square. We
Need to factorise the given numbers to find the sum.
First let us factorise \[\sqrt{}12\] ,
\[\sqrt{12} = \sqrt{2 \times 2 \times 3}\]
\[\sqrt{12} = \sqrt{2^{2} \times 3}\]
By taking the terms outside from the radical,
We get,
\[\sqrt{12} = 2\sqrt{3}\]
Now need to factorise \[\sqrt{27}\] ,
\[\sqrt{27} = \sqrt{3 \times 3 \times 3}\]
\[= \sqrt{3^{2} \times 3}\]
Then by taking the terms outside from the radical,
\[\sqrt{27} = 3\sqrt{3}\]
Now we can find the sum of \[\sqrt{12}\] and \[\sqrt{27}\] ,
\[\Rightarrow\sqrt{12} + \sqrt{27} = 2\sqrt{3} + 3\sqrt{3}\]
We know that \[a\sqrt{m} +b\sqrt{m} = \left( a + b \right)\sqrt{m}\]
Thus by adding
We get,
\[\sqrt{12} + \sqrt{27} = 5\sqrt{3}\]
Therefore the sum of the square root of \[12\] and the square root of \[27\] is \[5\sqrt{3}\] .
Final answer :
The square root of \[12\] plus the square root of \[27\] is \[5\sqrt{3}\]

Note: Square root of a number is a value in which it turns to the original number when it is multiplied by itself. Suppose \[a\] is a square root of \[b\] Then it is represented as \[a\ = \ \sqrt{b}\] . For example, \[4\] is The square root of \[16\] then it is represented as \[4 = \sqrt{16}\] .Mathematically, the symbol \[\sqrt{}\] is known as the radical sign which is used to represent the square root. It is basically one of the methods to solve the quadratic equation . In order to find the square root, we can use two methods
1.Long division method
2.Factorisation method
It’s easy to memorize the square root values of the numbers \[1\] to \[25\]. After that number we need to use the method to find the values.