Question

The product of $4\sqrt 6 $ and $3\sqrt {24} $ is?
a)124
b)134
c)144
d)154

Answer 1

Hint: Multiplication between two under rooted terms is the same as multiplying the two terms first and then applying under root. Multiply the non-under rooted terms first and then multiply the under rooted terms and match the correct option to it.

Complete step-by-step answer:
The given numbers are $4\sqrt 6 $ and $3\sqrt {24} $ .
So the product is:
\[4\sqrt 6 \times 3\sqrt {24} \]
\[ = (4 \times 3) \times (\sqrt 6 \times \sqrt {24} )\]
\[ = (12) \times (\sqrt {6 \times 24} )\]
\[ = 12 \times \sqrt {144} \]
\[ = 12 \times 12 = 144\]
Therefore, the product of the given numbers $4\sqrt 6 $ and $3\sqrt {24} $ is \[144\].
So, the correct answer is “Option C”.

Note: While calculating the product, always try to separate between general numbers and numbers under root, multiplying the powers correctly is very important in such sums.