Question

How do you simplify 5 square root of 8 times square root 18?

Answer 1

Hint: In this problem, we have to simplify 5 square root of 8 times square root 18. We can first convert the statement into a mathematical form to do simplification. We will get two roots, for which we can use the multiplication of two roots formula and multiply the terms, then we can multiply the remaining terms which are outside the root to get a simplified form.

Complete step by step solution:
We know that the given statement to be simplified is,
‘5 square root of 8 times root 18’
We can now convert it to a mathematical form, we get
\[5\sqrt{8}\sqrt{18}\]
Now we have to multiply the two roots in the above step.
We can use the multiplication of roots formula in the above step.
We know that the multiplication of roots formula is,
\[\sqrt{a}\sqrt{b}=\sqrt{ab}\] for \[a,b\ge 0\]
 We have non negative terms inside the root, we can use the above formula, we get
\[\Rightarrow 5\sqrt{8}\sqrt{18}=5\sqrt{8\times 18}\]
Now we can multiply the terms inside the root, we get
\[\Rightarrow 5\sqrt{144}\]
We know that \[144={{12}^{2}}\], we can substitute this value in the above step, we get
\[\Rightarrow 5\sqrt{{{\left( 12 \right)}^{2}}}\]
We can now cancel the square and the square root, we get
\[\Rightarrow 5\times 12=60\]

Therefore, the simplified value of the given expression is 60.

Note: Students should know how to multiply two roots, where the terms inside the root should be a non-negative term to get a real value. We can also know some perfect square values to simplify the problem directly. We should concentrate while converting the statement into a mathematical term.