Question

drag the numbers to the boxes to order them from least to greatest value.
-12√2
5.3
12
-8√3
3√5
-11.5

Explanation:

Step1: Calculate the approximate values of the radical expressions.

• For \(-12\sqrt{2}\): \(\sqrt{2}\approx1.414\), so \(-12\sqrt{2}\approx -12\times1.414 = -16.968\)
• For \(-8\sqrt{3}\): \(\sqrt{3}\approx1.732\), so \(-8\sqrt{3}\approx -8\times1.732 = -13.856\)
• For \(3\sqrt{5}\): \(\sqrt{5}\approx2.236\), so \(3\sqrt{5}\approx3\times2.236 = 6.708\)
• For \(-11\frac{1}{3}\), convert to decimal: \(-11\frac{1}{3}\approx -11.333\)

Step2: List all the numbers with their approximate values:

• \(-12\sqrt{2}\approx -16.968\)
• \(5.3\) (exact decimal)
• \(12\) (exact integer)
• \(-8\sqrt{3}\approx -13.856\)
• \(3\sqrt{5}\approx6.708\)
• \(-11\frac{1}{3}\approx -11.333\)

Step3: Order the numbers from least to greatest by comparing their approximate values.

• The smallest number is \(-12\sqrt{2}\approx -16.968\)
• Next is \(-8\sqrt{3}\approx -13.856\)
• Then \(-11\frac{1}{3}\approx -11.333\)
• Then \(5.3\)
• Then \(3\sqrt{5}\approx6.708\)
• The largest number is \(12\)

Answer:

\(-12\sqrt{2}\) < \(-8\sqrt{3}\) < \(-11\frac{1}{3}\) < \(5.3\) < \(3\sqrt{5}\) < \(12\)