Question

which expressions are listed in the simplest form ? Check all that apply

$5 \sqrt{3b}$
$2 \sqrt{21}$
$x \sqrt{8}$
$2 \sqrt{36}$
$\sqrt{5}$
$c \sqrt{12 {c2}^{?} }$

Answer 1

$5\sqrt{3b}\qquad\boxed{YES}\\\\2\sqrt{21}\qquad\boxed{YES}\\\\x\sqrt8=x\sqrt{4\cdot2}=x\sqrt4\cdot\sqrt2=2x\sqrt2\qquad\boxed{NOT}\\\\2\sqrt{36}=2\cdot6=12\qquad\boxed{NOT}\\\\\sqrt5\qquad\boxed{YES}\\\\c\sqrt{12c^2}=c\sqrt{4\cdot3\cdot c^2}=c\sqrt4\cdot\sqrt3\cdot\sqrt{c^2}=c\cdot2\cdot\sqrt3\cdot|c|=2c|c|\sqrt3\qquad\boxed{NOT}$

Answer 2

Here, you are required to check if each expression can be simplified further

Expression 1, 2 and 5 are in the simplest form already

5√3b

Can not be simplified further

2√21 = 2√7 × 3

aCan not be simplified further

x√8

= x × √4 × 2

= x × √4 × √2

= x × 2 × √2

= 2x√2

Can be simplified further

2√36

= 2 × √36

= 2 × 6

= 12

Can be simplified further

√5

Can not be simplified further

c√12c²

= c × √4×3×c²

= c × √4 × √3 × √c²

= c × 2 × √3 × c

= 2c²√3

Can be simplified further

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