Question

please do solve this maths question as soon as possible with full explanation​

Answer 1

Answer:

The correct answer is option D

Step-by-step explanation:

((27)^1/6 - (27/4)^1/2)^2

((3)^1/2 - (3)(3)^1/2)^2

Since,

(a - b)^2 = a^2 - 2ab + b^2

((3)^1/2)^2 - 2((3)^1/2)((3)^1/2)(3)/2 + (((3)(3)^1/2)/2)^2

3 - 9 + 27/4

(12 - 36 + 27)/4

3/4

Answer 2

Answer:

$( {(27)}^{ \frac{1}{6} } - {( \frac{27}{4}) }^{ \frac{1}{2} } )^{2}$

Using $(a-b)^2$ = $a^2+b^2-2ab$

$\\ ((27)^{ \frac{1}{6} } )^{2} + {(( \frac{27}{4} )^{ \frac{1}{2} } )}^{2} - 2 \times {(27)}^{ \frac{1}{6} } \times { (\frac{27}{4}) }^{ \frac{1}{2} } \\ \\ { (27) }^{ \frac{1}{3} } + \frac{27}{4} - 2 \times {(27)}^{ \frac{1}{6} } \times {(27)}^{ \frac{1}{2} } \times {(4)}^{ \frac{ - 1}{2} } \\ \\ 3 + \frac{27}{4} - 2 \times {( {(2)}^{2} )}^{ \frac{ - 1}{2} } \times {(27)}^{ \frac{1}{6} + \frac{1}{2} } \\ \\ 3 + \frac{27}{4} - {2}^{1} \times {2}^{ - 1} \times {(27)}^{ \frac{1 + 3}{6} } \\ \\ 3 + \frac{27}{4} - {2}^{(1 - 1)} \times {(27)}^{ \frac{4}{6} } \\ \\ 3 + \frac{27}{4} - {2}^{0} \times {(27)}^{ \frac{2}{3} } \\ \\ 3 + \frac{27}{4} - 1 \times {( {(27)}^{ \frac{1}{3} }) }^{2} \\ \\ 3 + \frac{27}{4} - {3}^{2} \\ \\ 3 + \frac{27}{4} - 9 \\ \\ \frac{12 + 27 - 36}{4} \\ \\ \frac{3}{4}$

Hope it helps