Question

Show that cube root 27×cube root 64=cube root 27×64

Answer 1

Hey there !

∛27 × ∛64 = ∛ ( 27 × 64 )

We will have to prove LHS = RHS

Cube root of 27 = 3

Cube root of 64 = 4

27 × 64 = 1728

cube root of 1728 = 12

3 × 4 = 12

12 = 12

LHS = RHS

Above equation is true

_________

Answer 2

$proving \: \: \sqrt[3]{27} \times \sqrt[3]{64} = \sqrt[3]{(27 \times 64)}$

$\red{ LHS}$ = $\sqrt[3]{27} \times \sqrt[3]{64}$
= 3 × 4

= 12

Now,
$\green{RHS}$ =

$\sqrt[3]{(27 \times 64)} \\ \\ = \sqrt[3]{1728} \\ \\ = 12$

Hence,
$\red{ LHS}$ = $\green{ RHS}$

verified