To find the value of [tex]\( \sqrt{12} \cdot \sqrt{18} \)[/tex], we can start by calculating the individual square roots and then multiplying them together.
1. First, find the square root of 12:
[tex]\[ \sqrt{12} \approx 3.464 \][/tex]
2. Next, find the square root of 18:
[tex]\[ \sqrt{18} \approx 4.243 \][/tex]
3. Multiply these two square roots together to find the product:
[tex]\[ \sqrt{12} \cdot \sqrt{18} \approx 3.464 \cdot 4.243 \approx 14.697 \][/tex]
With the product calculated, we can now compare it to the given choices to find the correct answer:
1. [tex]\( \sqrt{30} \)[/tex]:
[tex]\[ \sqrt{30} \approx 5.477 \][/tex]
2. [tex]\( 5\sqrt{6} \)[/tex]:
[tex]\[ 5\sqrt{6} \approx 5 \cdot 2.449 = 12.245 \][/tex]
3. [tex]\( 6\sqrt{5} \)[/tex]:
[tex]\[ 6\sqrt{5} \approx 6 \cdot 2.236 = 13.416 \][/tex]
4. [tex]\( 6\sqrt{6} \)[/tex]:
[tex]\[ 6\sqrt{6} \approx 6 \cdot 2.449 = 14.694 \][/tex]
Among the given choices, the value [tex]\( 6\sqrt{6} \approx 14.694 \)[/tex] is closest to the calculated product of [tex]\( \sqrt{12} \cdot \sqrt{18} \approx 14.697 \)[/tex].
Therefore, the correct answer is [tex]\( 6 \sqrt{6} \)[/tex].
