Question

please answer this...

Answer 1

Q1.

$a = 3( \frac{1}{3} \times \frac{11}{7} \times \frac{173205}{173} ) \\ \\ is \: \: same \: \: as \\ \\ a = 3 \times \frac{1}{3} \times \frac{11}{7} \times \frac{173205}{173}$

So yes, you can cancel the 3s
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Q2.

If you observe carefully the value of √3, you will find that it is not a long calculation.

√3 = 1.73205

So your calculation becomes

$a = 3( \frac{1}{3} \times \frac{11}{7} \times \frac{1732.05}{1.73205} ) \\ \\ a = \cancel{3} \times \frac{1}{ \cancel{3}} \times \frac{11}{7} \times 1000) \\ \\ a= \frac{11000}{7}$
You will rarely get a calculation like that (as you have done: 1732.05/1.73)
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2. Yes, you can cancel the 7. but do it step wise so you don't get confused. first expand the square term and then cancel:

$\frac{22}{7} \times {(7 \sqrt{2}) \: }^{2} \\ \\ = \frac{22}{7} \times 7 \sqrt{2} \times 7 \sqrt{2} \\ \\ = \frac{22}{ \cancel{7}} \times \cancel{7} \sqrt{2} \times 7 \sqrt{2} \\ \\ = 22 \times \sqrt{2} \times 7 \sqrt{2} \\ \\ = 22 \times 7 \times 2 = 308$


3. Again, you need to simplify first(means write the square term as multiplication) and then cancel:

$2( \frac{2}{7} \times {7}^{2} ) \\ \\ = 2 \times \frac{2}{7} \times 7 \times 7 \\ \\ = 2 \times \frac{2}{ \cancel{7}} \times \cancel{7} \times 7 \\ \\ = 28$