Question

choose from the following list of numbers to add to the number line. add numbers above the arrows. not all numbers will be needed. √12 √8 √20 √27 √46

Explanation:

Step1: Simplify $\sqrt{12}$

We factor 12 into $4\times3$, so $\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}$

Step2: Simplify $\sqrt{8}$

Factor 8 into $4\times2$, then $\sqrt{8}=\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}$

Step3: Simplify $\sqrt{20}$

Factor 20 into $4\times5$, so $\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$

Step4: Simplify $\sqrt{27}$

Factor 27 into $9\times3$, then $\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}$

Step5: Simplify $\sqrt{46}$

46 factors into $2\times23$, and neither 2 nor 23 is a perfect square, so $\sqrt{46}$ cannot be simplified further.

Answer:

• $\sqrt{12} = 2\sqrt{3}$
• $\sqrt{8} = 2\sqrt{2}$
• $\sqrt{20} = 2\sqrt{5}$
• $\sqrt{27} = 3\sqrt{3}$
• $\sqrt{46}$ (cannot be simplified)