Question

How do you simplify: 4 times the square root of 18?

Answer 1

Hint: In the given question we were asked to simplify 4 times the square root of 18. So, we will take prime factors of 18 and then we will simplify. After simplification, we can get an expression with or without root. So, let’s see how we can find out the solution.

Complete step by step solution:
The given problem statement is to simplify 4 times the square root of 18.
 So, we have to simplify 4 times the square root of 18, that is $4\sqrt{18}$ . Now we will take prime factors of 18
 $=4\sqrt{2\times 3\times 3}$
 $=4\sqrt{(3\times 3)\times 2}$
3 appears two times so we will make it a square
 $=4\sqrt{{{3}^{2}}\times 2}$
By applying the rule $\sqrt{{{a}^{2}}}=a$
 $=4\times 3\sqrt{2}$
 $=12\sqrt{2}$
So, after simplifying 4 times the square root of 18 is $12\sqrt 2$

Note: In the given question we were asked to simplify 4 times the square root of 18 that’s why we solved $4\sqrt{18}$ if we were asked to solve the square root to 4 times of 18 then we have to solve for $\sqrt{4\times 18}$. For which the solution would be different.
In the above solution, the number 3 appears two times that’s why we can make it a square. After which we applied a simple rule of $\sqrt{{{a}^{2}}}=a$ and so we can take the 3 out of square root. The 2 has no pair left that’s why in the final answer we kept 2 inside the square root.