Question

How do you simplify $\sqrt {18}$ without a calculator ?

Answer 1

Hint : Start the solution by explaining how a number can escape a root. After this step try to write the given number in the root as the product of factors of prime number. After this you can bring the like terms together and then if the square of a term exists you can shift it outside removing it’s square respectively.

Complete step-by-step answer :
So we have to find the square root of $\sqrt {18}$ without using a calculator.
As $\sqrt {18}$ is not a perfect square we need some steps to simplify it.
To find the answer we need to follow some tricks or rules to make the sum a little easier.
The first thing to do is prime factorization. i.e. we need to write the number inside the root as a product of prime numbers.
So following the above step we get
$\sqrt {18} = \sqrt {3 \times 3 \times 2}$
solving further we get
$\sqrt {18} = \sqrt {{3^2} \times 2}$
Now since ${3^2}$ or 9 is a perfect square we can take that term outside the root as it is present in product form. So we get
$\sqrt {18} = 3\sqrt 2$
Since there are no perfect square present in the root now, this is the final answer of $\sqrt {18}$
So, the correct answer is “ $\sqrt {18} = 3\sqrt 2$ ”.

Note : Since $\sqrt {18}$ was a smaller number we used the process of prime factorization. But if the number given is very large then this process will be time consuming. Instead you can find out if the number is a multiple of any square of a number. You can use this process in the above sum as well.