Question

enter the values for the variables that give the correct simplified expressions, x = ≥ 0.\\(\sqrt{50x^2} = \sqrt{25 \cdot 2 \cdot x^2} = 5x\sqrt{b}\\)\\(b = \square\\)\\(\sqrt{32x} = \sqrt{16 \cdot 2 \cdot x} = c\sqrt{2x}\\)\\(c = \square\\)\\(\sqrt{18n} = \sqrt{9 \cdot 2 \cdot n} = e\sqrt{2n}\\)\\(e = \square\\)\\(\sqrt{72x^2} = \sqrt{36 \cdot 2 \cdot x^2} = gx\sqrt{2}\\)\\(g = \square\\)

Explanation:

Step1: Simplify $\sqrt{50x^2}$

$\sqrt{50x^2}=\sqrt{25\cdot2\cdot x^2}=\sqrt{25}\cdot\sqrt{x^2}\cdot\sqrt{2}=5x\sqrt{2}$

Step2: Identify $b$

Compare $5x\sqrt{2}$ with $5x\sqrt{b}$, so $b=2$.

Step3: Simplify $\sqrt{32x}$

$\sqrt{32x}=\sqrt{16\cdot2\cdot x}=\sqrt{16}\cdot\sqrt{2x}=4\sqrt{2x}$

Step4: Identify $c$

Compare $4\sqrt{2x}$ with $c\sqrt{2x}$, so $c=4$.

Step5: Simplify $\sqrt{18n}$

$\sqrt{18n}=\sqrt{9\cdot2\cdot n}=\sqrt{9}\cdot\sqrt{2n}=3\sqrt{2n}$

Step6: Identify $e$

Compare $3\sqrt{2n}$ with $e\sqrt{2n}$, so $e=3$.

Step7: Simplify $\sqrt{72x^2}$

$\sqrt{72x^2}=\sqrt{36\cdot2\cdot x^2}=\sqrt{36}\cdot\sqrt{x^2}\cdot\sqrt{2}=6x\sqrt{2}$

Step8: Identify $g$

Compare $6x\sqrt{2}$ with $gx\sqrt{2}$, so $g=6$.

Answer:

$b=2$, $c=4$, $e=3$, $g=6$