Question

question 1
match each radical on the left to its simplified radical on the right.
\\(\sqrt{27}\\) \t\t\t\t\t a. \\(10\sqrt{3}\\)
\\(\sqrt{100}\\) \t\t\t\t\t b. \\(3\sqrt{3}\\)
\\(\sqrt{300}\\) \t\t\t\t\t c. \\(4\sqrt{3}\\)
\\(\sqrt{48}\\) \t\t\t\t\t d. 10

Explanation:

Step1: Simplify $\sqrt{27}$

Factor 27: $27 = 9\times3$. Then $\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}$, so $\sqrt{27}$ matches b.

Step2: Simplify $\sqrt{100}$

$\sqrt{100} = 10$ (since $10^2 = 100$), so $\sqrt{100}$ matches d.

Step3: Simplify $\sqrt{300}$

Factor 300: $300 = 100\times3$. Then $\sqrt{300}=\sqrt{100\times3}=\sqrt{100}\times\sqrt{3}=10\sqrt{3}$, so $\sqrt{300}$ matches a.

Step4: Simplify $\sqrt{48}$

Factor 48: $48 = 16\times3$. Then $\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}$, so $\sqrt{48}$ matches c.

Answer:

$\sqrt{27}$ - b. $3\sqrt{3}$
$\sqrt{100}$ - d. $10$
$\sqrt{300}$ - a. $10\sqrt{3}$
$\sqrt{48}$ - c. $4\sqrt{3}$