Question

Which choices are equivalent to the expression below? Check all that apply. 5 square root 3

Answer 1

Option A: $\sqrt{75}$

Option C: $\sqrt{15} \cdot \sqrt{5}$

Option F: $\sqrt{25} \cdot \sqrt{3}$

Solution:

Given expression is $5 \sqrt{3}$.

Option A: $\sqrt{75}$

$\sqrt{75}=\sqrt{25\times3}$

       $=\sqrt{5^2\times3}$

       $=5\sqrt{3}$

Hence $\sqrt{75}$ is equivalent expression of $5 \sqrt{3}$.

Option B: $\sqrt{45}$

$\sqrt{45}=\sqrt{9\times5}$

       $=\sqrt{3^2\times5}$

       $=3\sqrt{5}$

Hence $\sqrt{45}$ is not equivalent expression of $5 \sqrt{3}$.

Option C: $\sqrt{15} \cdot \sqrt{5}$

$\sqrt{15} \cdot \sqrt{5}=\sqrt{15\times5}$

              $=\sqrt{75}$

              $=5\sqrt{3}$    (proved in option A)

Hence $\sqrt{15} \cdot \sqrt{5}$ is equivalent expression of $5 \sqrt{3}$.

Option D: $\sqrt{3} \cdot \sqrt{5}$

$\sqrt{3} \cdot \sqrt{5}=\sqrt{3\times5}$

            $=\sqrt{15}$

Hence $\sqrt{3} \cdot \sqrt{5}$ is not equivalent expression of $5 \sqrt{3}$.

Option E: 75

75 is a whole number.

Hence 75 is not equivalent expression of $5 \sqrt{3}$.

Option F: $\sqrt{25} \cdot \sqrt{3}$

$\sqrt{25} \cdot \sqrt{3}=\sqrt{25\times3}$

              $=\sqrt{75}$

              $=5\sqrt{3}$    (proved in option A)

Hence $\sqrt{25} \cdot \sqrt{3}$ is equivalent expression of $5 \sqrt{3}$.

Therefore, $\sqrt{75},\ \ \sqrt{15} \cdot \sqrt{5}, \ \ \sqrt{25} \cdot \sqrt{3}$ are all equivalent expressions of $5 \sqrt{3}$.