Question

How do you find the value of 3 square root 27?

Answer 1

Hint: In the above question, you were asked to find the value of 3 square root 27. To solve this problem, you can use the formula of $\sqrt {ab} = \sqrt a \sqrt b$ but this formula is only applicable when a and b are greater than 0. So, let us see how we can solve this problem.

Complete Step by Step Solution:
In the given problem, we have to find the value of $3\sqrt {27}$. For solving this problem, we will use $\sqrt {ab} = \sqrt a \sqrt b$.
So, $3\sqrt {27}$ can also be written as
 $= 3\sqrt {{3^2}.3}$
 $= 3\sqrt {{3^2}} \sqrt 3$
After taking 3 square out of square root we get,
 $= 3.3\sqrt 3$
After calculating the above expression, we get,
 $= 9\sqrt 3$

Therefore, the value of $3\sqrt {27}$ is $9\sqrt 3$.

Note:
In the above solution, we factored 27 which is inside the root. Factor of 27 is 3 x 3 x 3. So, we take ${3^2}$ out of the square root. And then calculated the value. Also, we used a formula of $\sqrt {ab} = \sqrt a \sqrt b$, this formula can only be applied when a and b are greater than or equal to zero. In this case, it is ${3^2}$ and 3 which is, of course, greater than zero. So, we applied that formula.