Question

Please help me .....
$\frac{80}{90} - \sqrt{50} \times {19}^{2} \div {23}^{2}$
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Answer 1

Answer:

$\implies \dfrac{80}{90}-\sqrt{50} \times 19^2 \div 23^2$

Order of operations (PEDMAS)

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Following the order of operations,
Carry out the exponents (and radicals) first:

$\implies \dfrac{80}{90}-\sqrt{25 \cdot 2} \times 361 \div 529$

$\implies \dfrac{80}{90}-5\sqrt{2} \times 361 \div 529$

Now the multiplication and division (from left to right):

$\implies \dfrac{8}{9}-1805\sqrt{2} \div 529$

$\implies \dfrac{8}{9}-\dfrac{1805\sqrt{2}}{529}$

Convert the fractions so that their denominators are the same:

$\implies \dfrac{8 \times 529}{9 \times 529}-\dfrac{1805\sqrt{2} \times 9}{529 \times9}$

$\implies \dfrac{4232}{4761}-\dfrac{16245\sqrt{2}}{4761}$

Answer as a fraction:

$\implies \dfrac{4232-16245\sqrt{2}}{4761}$

Answer as a number:

$\implies -3.936546801... = -3.9\: \textsf{(nearest tenth)}$