15 Select the correct answer. What is the estimated value of (2sqrt (12)cdot 3sqrt (5))/(sqrt (30)cdot sqrt (36)) A. 0.71 B. 1.41 C. 2 D. 2.45

To solve the expression \(\frac{2\sqrt{12} \cdot 3\sqrt{5}}{\sqrt{30} \cdot \sqrt{36}}\), we need to simplify each part of the expression step by step.<br /><br />First, let's simplify the numerator:<br />\[ 2\sqrt{12} \cdot 3\sqrt{5} \]<br /><br />We know that \(\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}\). So,<br />\[ 2\sqrt{12} = 2 \cdot 2\sqrt{3} = 4\sqrt{3} \]<br /><br />Thus, the numerator becomes:<br />\[ 4\sqrt{3} \cdot 3\sqrt{5} = 12\sqrt{15} \]<br /><br />Next, let's simplify the denominator:<br />\[ \sqrt{30} \cdot \sqrt{36} \]<br /><br />We know that \(\sqrt{36} = 6\). So,<br />\[ \sqrt{30} \cdot \sqrt{36} = \sqrt{30} \cdot 6 = 6\sqrt{30} \]<br /><br />Now, we can write the original expression as:<br />\[ \frac{12\sqrt{15}}{6\sqrt{30}} \]<br /><br />We can simplify this fraction by canceling out the common factor of 6 in the numerator and the denominator:<br />\[ \frac{12\sqrt{15}}{6\sqrt{30}} = 2 \cdot \frac{\sqrt{15}}{\sqrt{30}} \]<br /><br />Next, we simplify \(\frac{\sqrt{15}}{\sqrt{30}}\):<br />\[ \frac{\sqrt{15}}{\sqrt{30}} = \sqrt{\frac{15}{30}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \]<br /><br />So, the expression becomes:<br />\[ 2 \cdot \frac{\sqrt{2}}{2} = \sqrt{2} \]<br /><br />We know that \(\sqrt{2} \approx 1.414\).<br /><br />Therefore, the estimated value of the expression is:<br />\[ \boxed{1.41} \]<br /><br />So, the correct answer is:<br />B. 1.41