Question

a number line is shown.

which values are ordered least to greatest when plotted on the number line?

a. \\( \sqrt{120} \\), \\( 0.5\sqrt{170} \\), \\( 2\sqrt{50} \\)

b. \\( 0.5\sqrt{170} \\), \\( \sqrt{120} \\), \\( 2\sqrt{50} \\)

c. \\( 2\sqrt{50} \\), \\( \sqrt{120} \\), \\( 0.5\sqrt{170} \\)

d. \\( \sqrt{120} \\), \\( 2\sqrt{50} \\), \\( 0.5\sqrt{170} \\)

Explanation:

Step1: Simplify each expression

• For \(\sqrt{120}\): \(120 = 4\times30\), so \(\sqrt{120}=\sqrt{4\times30}=2\sqrt{30}\approx2\times5.477 = 10.954\)
• For \(0.5\sqrt{170}\): \(0.5\sqrt{170}=\frac{\sqrt{170}}{2}\), \(\sqrt{170}\approx13.038\), so \(\frac{\sqrt{170}}{2}\approx6.519\)
• For \(2\sqrt{50}\): \(50 = 25\times2\), so \(2\sqrt{50}=2\sqrt{25\times2}=2\times5\sqrt{2}=10\sqrt{2}\approx10\times1.414 = 14.14\)

Step2: Order the simplified values

• \(0.5\sqrt{170}\approx6.519\)
• \(\sqrt{120}\approx10.954\)
• \(2\sqrt{50}\approx14.14\)

So the order from least to greatest is \(0.5\sqrt{170}\), \(\sqrt{120}\), \(2\sqrt{50}\)

Answer:

B. \(0.5\sqrt{170}\), \(\sqrt{120}\), \(2\sqrt{50}\)