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Answer 1

$\boxed{\underline{\textsf{Solutions :}}}$

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Two cubes are of 6 cm side each.

When both the cubes are joined end to end,

 • length ( l ) = 6 + 6 cm = 12 cm

 • breadth ( b ) = 6 cm

 • height ( h ) = 6 cm

Therefore, the surface area of the resulting cuboid

 = 2 ( lb + bh + hl ) cm²

 = 2 { (12*6) + (6*6) + (6*12) } cm²

 = 2 (72 + 36 + 72) cm²

 = 2*180 cm²

 = 360 cm²

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Now, (4√3 - 3√5)²

 = (4√3)² - (2 * 4√3 * 3√5) + (3√5)²

    { since (a - b)² = a² - 2ab + b² }

       = (16*3) - 24√15 + (9*5)

          = 48 - 24√15 + 45

             = 93 - 24√15 ,

which is the required simplification.

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Let us take $x=0.4\bar{7}$

       ➨ x = 0.4777... -----(1)

    So, 10x = 4.777... -----(2)

and 100x = 47.777... -----(3)

Now, (3) - (2) ➨

100x - 10x = 47.777... - 4.777...

 ➨ 90x = 43

 ➨ x = $\frac{43}{90}$ ,

which is in the required $\dfrac{p}{q}$ form.