Question

How do you simplify the square root of 6 times square root of 60?

Answer 1

Hint: In this problem, we have to simplify the square root of 6 times the square root of 60. We have to write this expression in mathematical form to simplify it. Then we have to simplify the number inside the square root to its reduced form and then multiply the reduced numbers to get the final square root value.

Complete step by step answer:
Here, we have to simplify the square root of 6 times the square root of 60.
We can write the above expression in mathematical form, we get
We have to simplify \[\sqrt{6\times 60}\].
As we have square root of 6 ‘times’ square root of 60, we have multiplied the numbers of square root 6 and square root 60.
Now, we can simplify the mathematical expression.
\[\Rightarrow \sqrt{6\times 60}\]
We know that 6 is 3 times of 2 and 60 is 10 times of 6, applying this in the above step, we get
\[\Rightarrow \sqrt{3\times 2\times 10\times 6}\]
We can again reduce 10 and 6 to its simplified form, we get
\[\begin{align}
  & \Rightarrow \sqrt{3\times 2\times 5\times 2\times 3\times 2} \\
 & \Rightarrow \sqrt{{{3}^{2}}\times {{2}^{2}}\times 5\times 2} \\
 & \Rightarrow \sqrt{{{\left( 3\times 2 \right)}^{2}}}\times \sqrt{5\times 2} \\
 & \Rightarrow {{\left( 3\times 2 \right)}^{2\times \dfrac{1}{2}}}\times \sqrt{5\times 2} \\
\end{align}\]
Now we can cancel the similar terms in the power, to get
\[\begin{align}
  & \Rightarrow 3\times 2\sqrt{5\times 2} \\
 & \Rightarrow 6\sqrt{10} \\
\end{align}\]
Therefore, the simplified form of \[\sqrt{6\times 60}\] is \[6\sqrt{10}\].

Note:
Students make mistakes in converting the expression into the mathematical form, which should be concentrated. Only if the mathematical conversion of the respective sentence is correct, the solution of it is accepted. We should know the multiplication tables to solve these types of problems.