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Vinvika [58]
2 years ago
13

Simplify each expression using the proper order of operations. please help thank you so much :)

Mathematics
1 answer:
Tasya [4]2 years ago
7 0

Answer:

\frac{41 - 3^2}{\sqrt{36} * 3 - 26} = -4

12 + 3\sqrt{8} * (9 - 2) = 12 + 42 \sqrt{2}

\frac{28 - (7^2 + 3)}{-13 + 3 * 5} = -12

7^2 - 5* 8+1 = 10

(2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1 = -18

Step-by-step explanation:

<em>Required: Solve the expressions using proper operation order</em>

To solve this, we'll make use of BODMAS

--------------------------------------------------------------------------------------------------------

\frac{41 - 3^2}{\sqrt{36} * 3 - 26}

Evaluate all squares and square roots

\frac{41 - 3*3}{\sqrt{36} * 3 - 26}

\frac{41 - 3*3}{6 * 3 - 26}

Evaluate the numerator (Start by multiplying 3 * 3)

\frac{41 - 9}{6 * 3 - 26}

Subtract 9 from 41

\frac{32}{6 * 3 - 26}

Evaluate the denominator (Start by multiplying 6 * 3)

\frac{32}{18 - 26}

\frac{32}{-8}

Divide 32 by -8

-4

Hence;

\frac{41 - 3^2}{\sqrt{36} * 3 - 26} = -4

--------------------------------------------------------------------------------------------------------

12 + 3\sqrt{8} * (9 - 2)

Start by evaluating the bracket

12 + 3\sqrt{8} * 7

Then evaluate the multiplication

12 + 21\sqrt{8}

Simplify the square root

12 + 21\sqrt{4 * 2}

Split the square root

12 + 21\sqrt{4} * \sqrt{2}

Take Square root of 4

12 + 21 * 2} * \sqrt{2}

12 + 42 \sqrt{2}

Hence;

12 + 3\sqrt{8} * (9 - 2) = 12 + 42 \sqrt{2}

--------------------------------------------------------------------------------------------------------

\frac{28 - (7^2 + 3)}{-13 + 3 * 5}

Evaluate 7²

\frac{28 - (49 + 3)}{-13 + 3 * 5}

Evaluate all expression in the bracket

\frac{28 - (52)}{-13 + 3 * 5}

\frac{28 - 52}{-13 + 3 * 5}

Evaluate 3 * 5

\frac{28 - 52}{-13 + 1 5}

\frac{-2 4}{2}

-12

Hence;

\frac{28 - (7^2 + 3)}{-13 + 3 * 5} = -12

--------------------------------------------------------------------------------------------------------

7^2 - 5* 8+1

Evaluate 7²

49 - 5* 8+1

Evaluate 5 * 8

49 - 40 + 1

10

7^2 - 5* 8+1 = 10

--------------------------------------------------------------------------------------------------------

(2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1

Evaluate all square root and cube root

(2 * 4) - (3 * 9) + 1

Solve the expressions in bracket

8 - 27 + 1

-18

Hence;

(2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1 = -18

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