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follow BODMAS rule to solve this question, as per the order given below,

Step-1-Parts of an equation ENCLOSED in 'Brackets' must be solved first,

Step-2-Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4-Last but not LEAST, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

The given expression is:

$(12\; \TIMES 35\% \;of\;1000 - \sqrt[3]{{117649}} \div 7 = a + 32)$

$(\Rightarrow 12 \times \frac{{35}}{{100}} \times 1000 - 49 \div 7 = a + 32)$

⇒ 12 × 350 - 7 = a + 32

⇒ 4200 - 7 = a + 32

⇒ 4193 = a + 32

⇒ a = 4193 – 32

FORMULA: (a + b)² = a² + b²  + 2ab

The given surd is: 12 + 6√3

Let us write the surd as (a + √b)²

Expansion of (a + √b)² is given as:

(a + √b)² = a² + b + 2a√b----------(1)

By comparing 2a√b TERM of this EQUATION with that of the given surd, we get

a = 3 and b = √3

So, we can write the given expression as: (3 + √3)²

Follow BODMAS rule to SOLVE this question, as PER the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved NEXT,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

98.8 ×$ 4032 ÷ 27.89% of 599 = 16 ×$ 339.7 ÷ 17.2 + ? + 80.1

Taking Approximate values as,

98.8 ≈ 99, 27.89 ≈ 28, 599 ≈ 600, 339.7 ≈ 340, 17.2 ≈ 17, 80.1 ≈ 80

⇒ 99 ×$ 4032 ÷ 28% of 600 = 16 ×$ 340 ÷ 17 + ? + 80

⇒ 99 ×$ 4032 ÷ 0.28 ×$ 600 = 16 ×$ 20 + ? + 80

⇒ 99 ×$ 24 = 320 + ? + 80

Follow BODMAS rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be SOLVED first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved NEXT,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

2520 ÷ 6² × 8.5 – √5776 + 31² = ?

⇒ 2520 ÷ 36 × 8.5 – 76 + 961 = ?

Applying BODMAS Rule;

⇒ 70 × 8.5 – 76 + 961 = ?

⇒ 595 – 76 + 961 = ?

$(\begin{array}{l}\frac{2}{5} \TIMES \frac{4}{5} - \frac{8}{5} \div \frac{3}{5} + \frac{6}{5} \times \frac{9}{5} \div \frac{3}{5} = \;?\\ \Rightarrow \frac{2}{5} \times \frac{4}{5} - \frac{8}{5} \times \frac{5}{3} + \frac{6}{5} \times \frac{9}{5} \times \frac{5}{3} = \;?\end{array})$

$(\begin{array}{l} \Rightarrow \frac{8}{{25}} - \frac{8}{3} + \frac{{18}}{5} = \;?\\ \Rightarrow \frac{{98}}{{25}} - \frac{8}{3} = \;?\end{array})$

∴ ? = 94/75

Follow BODMAS rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved NEXT,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

105.01% of 7498.97 - 3/7% of 5739.9 + 20.15 = ?

Taking the APPROXIMATE VALUES as,

105.01 ≈ 105, 7498.97 ≈ 7500, 5739.9 ≈ 5740, 20.15 ≈ 20

105% of 7500 - 3/7% of 5740 + 20 = ?

⇒ 7875 - 24.6 + 20 = ?

Follow BODMAS rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

(0.1458 ÷ 0.2)^1/3 ÷ (102.4 × 10)^1/5 × (0.5 × 4)⁵ + 0.9 = [(9)^{? + 3}] ÷ 10

⇒ (0.729)^1/3 ÷ (1024)^1/5 × (2)⁵ + 0.9 = [(9)^{? + 3}] ÷ 10

⇒ 0.9 ÷ 4 × 32 + 0.9 = [(9)^{? + 3}] ÷ 10

⇒ 7.2 + 0.9 = [(9)^{? + 3}] ÷ 10

⇒ 81 = [(9)^{? + 3}]

Follow BODMAS rule to solve this question, as PER the order given below,

Step-1 – Parts of an equation ENCLOSED in 'Brackets' must be SOLVED FIRST, and in the bracket, the BODMAS rule must be followed,

Step-2 – Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3 – Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4 – Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

95.975^3.5 ÷ 12.001^3.5 × 7.998^1.5 ÷ 63.979² = ?

(? We have to find the approximate value, so we’ll take the values of 95.975 as 96, 12.001 as 12, 7.998 as 8 and 63.979 as 64)

⇒ 96^3.5 ÷ 12^3.5 × 8^1.5 ÷ 64² = ?

$(\Rightarrow \;{\left( {\frac{{96}}{{12}}} \right)^{3.5}} \times \frac{{{8^{1.5}}}}{{{{\left( {{8^2}} \right)}^2}}}\; = \;?)$

$(\Rightarrow \;{8^{3.5}} \times \frac{{{8^{1.5}}}}{{{8^4}}}\; = \;?)$

By using these laws of indices:

Follow BODMAS rule to solve this question, as PER the order given below,

Step-1- Parts of an equation ENCLOSED in 'Brackets' must be solved first, and in the bracket, the BODMAS rule must be followed,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4-Last but not LEAST, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated

Given Expression is,

$(\sqrt {\sqrt {10000\; \div 4} + \sqrt {961} } = {\LEFT( ? \right)^2})$

$(\Rightarrow \sqrt {\sqrt {2500} + \sqrt {961} } = {\left( ? \right)^2})$

$(\Rightarrow \sqrt {\sqrt {{5^2}\; \times \;{{10}^2}} + \sqrt {{{31}^2}} } = {\left( ? \right)^2})$

$(\Rightarrow \sqrt {50 + 31} = {\left( ? \right)^2})$

$(\Rightarrow \sqrt {81} = {\left( ? \right)^2})$

⇒ 9 = (?)²

⇒ ? = √9

$( \frac{{489.1385\; \times \;0.0493\; \times \;1.966}}{{0.0873\; \times \;92.581\; \times \;99.749}}\; = \;?)$

Follow BODMAS rule to solve this question, as per the ORDER given below:

Step-1: Parts of an equation ENCLOSED in 'Brackets' must be solved FIRST, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Here, 489.1385 ≈ 489

0.0493 ≈ 0.05

1.966 ≈ 2

0.0873 ≈ 0.09

92.581 ≈ 92.6

99.749 ≈ 100

Then, given EXPRESSION will become

$(\frac{{489\; \times \;0.05\; \times \;2}}{{0.09\; \times \;92.6\; \times \;100}} \approx \;?)$

⇒ ? ≈ 0.06

$(\sqrt {1200} \; + \;\frac{{3.001}}{{4.987}}\;)$ of 1899.992 = ?

Follow BODMAS rule to solve this question, as per the ORDER given below:

Step-1: Parts of an equation ENCLOSED in 'Brackets' must be solved FIRST, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

We can write the given values as:

√1200 ≈ 20 × 1.7 = 34

3.001 ≈ 3

4.987 ≈ 5

1899.992 ≈ 1900

Therefore, the given expression will be

⇒ ? = 34 + $(\frac{3}{5})$ × 1900

⇒ ? = 1174

Given, price of a COMMODITY decreased by 10% each year.

The present price is RS. 1000.

Price after 1 year = 1000 – 10% of 1000 = 0.9 × 1000 = Rs. 900

Price after 2 years = 900 – 10% of 900 = 0.9 × 900 = Rs. 810

Price after 3 years = 810 – 10% of 810 = 0.9 × 810 = Rs. 729

Total DECREASE in price = 1000 – 729 = Rs. 271

212 + 88 × 105 ÷ ? – 104 = 773 – 15²

⇒ 212 + 88 × 105 ÷ ? – 104 = 773 – 225

⇒ 88 × 105 ÷ ? = 773 – 225 + 104 – 212

⇒ 88 × 105 ÷ ? = 440

⇒ ? = (88 × 105) ÷ 440

⇒ ? = 105 ÷ 5

374562 × 64 = ?² × 777

⇒ ? ² = (374562 × 64)/777

⇒ ? = √(30851.95)

⇒ ? ≈ 175

The GIVEN EXPRESSION:

$(\frac{{208}}{{13}} \times \frac{{17}}{{16}} \times ? = 4046)$

$(= \frac{{13}}{{13}} \times 17 \times ? = 4046)$

= 17 ×? = 4046