Question

which number is equivalent to $5\sqrt{8} \cdot 3\sqrt{4}$?
(a) $15\sqrt{2}$
(b) $60\sqrt{2}$
(c) $30\sqrt{3}$
(d) $60\sqrt{3}$

Explanation:

Step1: Simplify the square roots

First, simplify \( \sqrt{8} \) and \( \sqrt{4} \). We know that \( \sqrt{8}=\sqrt{4\times2}=\sqrt{4}\times\sqrt{2} = 2\sqrt{2} \) and \( \sqrt{4} = 2 \).

Step2: Substitute the simplified roots into the original expression

Substitute these back into the original expression \( 5\sqrt{8}\cdot3\sqrt{4} \). So we have \( 5\times(2\sqrt{2})\times3\times2 \).

Step3: Multiply the coefficients and the square roots separately

First, multiply the coefficients: \( 5\times2\times3\times2= 60 \). Then, the square root part is \( \sqrt{2} \) (since we already simplified \( \sqrt{8} \) to \( 2\sqrt{2} \) and the other square root is just a coefficient now). Combining these, we get \( 60\sqrt{2} \).

Answer:

b. \( 60\sqrt{2} \)