Question

find the product of 3root 2. 4root 2 . 12 root 32

Answer 1

$\huge\tt{{\orange{Republic}}_{\blue{Happy}} {\green{Day}}}$



3√2 × 4√2 × 12√32

= 3√2 × 4√2 × 12√( 2 × 2 × 2 × 2 × 2 )

= 3√2 × 4√2 × 12√( $<u>2 × 2</u>$ × 2 × 2 × 2 )

= 3√2 × 4√2 × 2 × 12√( $<u>2 × 2</u>$ × 2 )

= 3√2 × 4√2 × 2 × 2 × 12√2

= 3√2 × 4√2 × 48√2

= ( 3 × 4 × 48 ) × ( √2 × √2 × √2 )

= 576 × ( 2√2 )

= $<b>1152√2</b>$

Answer 2

$\large\mathfrak{\underline{\underline{Solution :}}}$

$\sf{3{\sqrt{2}} × 4{\sqrt{2}} × 12{\sqrt{32}}}$

$\sf{\implies 3{\sqrt{2}} × 4{\sqrt{2}} × 12{\sqrt{2^5}}}$

$\sf{\implies 3{\sqrt{2}} × 4{\sqrt{2}} × 2 × 2 × 12{\sqrt{2}}}$

$\sf{\implies 3{\sqrt{2}} × 4{\sqrt{2}} × 48{\sqrt{2}}}$

$\sf{\implies 3 × 4 × 48 × {\sqrt{2 × 2 × 2}}}$

$\sf{\implies 576 × 2{\sqrt{2}}}$

$\sf\red{\implies 1152{\sqrt{2}}}$