Question

Which choice is equivalent to the expression below? √27 - √12 + √48

Answer 1

Answer:

D

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplifying each radical

$\sqrt{27}$

= $\sqrt{9(3)}$ = $\sqrt{9}$ × $\sqrt{3}$ = 3$\sqrt{3}$

$\sqrt{12}$

= $\sqrt{4(3)}$ = $\sqrt{4}$ × $\sqrt{3}$ = 2$\sqrt{3}$

$\sqrt{48}$

= $\sqrt{16(3)}$ = $\sqrt{16}$ × $\sqrt{3}$ = 4$\sqrt{3}$

Then

3$\sqrt{3}$ - 2$\sqrt{3}$ + 4$\sqrt{3}$

= 5$\sqrt{3}$ → D