Question

Which expression is equivalent to (21/2 x 2 3/4)^2

Answer 1

$\left(2\dfrac{1}{2}\cdot2\dfrac{3}{4}\right)^2=\left(\dfrac{2\cdot2+1}{2}\cdot\dfrac{2\cdot4+3}{4}\right)^2=\left(\dfrac{5}{2}\cdot\dfrac{11}{4}\right)^2=\left(\dfrac{55}{8}\right)^2\\\\=\dfrac{55^2}{8^2}=\dfrac{3025}{64}$

Answer 2

ANSWER

$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = 47 \frac{17}{64}$


EXPLANATION

To find the expression that is equivalent to
$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2}$

we need to simplify it.


We convert the mixed numbers to improper fraction as follows.



$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = ( \frac{2 \times 2 + 1}{2} \times \frac{2 \times 4 + 3}{4} ) ^{2}$


This will give us,

$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = ( \frac{4 + 1}{2} \times \frac{8 + 3}{4} )^{2}$


$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = ( \frac{5}{2} \times \frac{11}{4} )^{2}$


We multiply the expression in the parenthesis on the right hand side to obtain,

$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = ( \frac{55}{8} )^{2}$


We share the exponent for the numerator and the denominator separately.


$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = \frac{ {55}^{2} }{ {8}^{2} }$



This simplifies to,


$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = \frac{ {3025} }{ {64}}$


We write the final answer as a mixed number to obtain,

$(2 \frac{1}{2} \times 2 \frac{3}{4} ) ^{2} = 47 \frac{17}{64}$