Question

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

Explanation:

Step1: Recall square root definition

The square root of a number \( x \), denoted \( \sqrt{x} \), is a value \( y \) such that \( y^2 = x \). We need to find which \( \sqrt{x} = 12 \), so we solve \( y^2 = x \) where \( y = 12 \), so \( x = 12^2 \).

Step2: Calculate \( 12^2 \)

\( 12^2 = 144 \), so \( \sqrt{144} = 12 \) because \( 12\times12 = 144 \). We can check the others: \( \sqrt{24}\approx4.9 \), \( \sqrt{48}\approx6.9 \), \( \sqrt{120}\approx10.95 \), none equal 12.

Answer:

\( \sqrt{144} \)