Question

which expression has a value of 12? \\(sqrt{24}\\) \\(sqrt{48}\\) \\(sqrt{120}\\) \\(sqrt{144}\\)

Explanation:

Step1: Calculate $\sqrt{24}$

Factor 24: $24 = 4\times6$. Then $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\approx2\times2.45 = 4.9$, not 12.

Step2: Calculate $\sqrt{48}$

Factor 48: $48 = 16\times3$. Then $\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}\approx4\times1.73 = 6.92$, not 12.

Step3: Calculate $\sqrt{120}$

Factor 120: $120 = 4\times30$. Then $\sqrt{120}=\sqrt{4\times30}=\sqrt{4}\times\sqrt{30}=2\sqrt{30}\approx2\times5.48 = 10.96$, not 12.

Step4: Calculate $\sqrt{144}$

We know that $12\times12 = 144$, so $\sqrt{144}=12$.

Answer:

$\sqrt{144}$