Answer:
[tex]\frac{41 - 3^2}{\sqrt{36} * 3 - 26} = -4[/tex]
[tex]12 + 3\sqrt{8} * (9 - 2) = 12 + 42 \sqrt{2}[/tex]
[tex]\frac{28 - (7^2 + 3)}{-13 + 3 * 5} = -12[/tex]
[tex]7^2 - 5* 8+1 = 10[/tex]
[tex](2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1 = -18[/tex]
Step-by-step explanation:
Required: Solve the expressions using proper operation order
To solve this, we'll make use of BODMAS
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[tex]\frac{41 - 3^2}{\sqrt{36} * 3 - 26}[/tex]
Evaluate all squares and square roots
[tex]\frac{41 - 3*3}{\sqrt{36} * 3 - 26}[/tex]
[tex]\frac{41 - 3*3}{6 * 3 - 26}[/tex]
Evaluate the numerator (Start by multiplying 3 * 3)
[tex]\frac{41 - 9}{6 * 3 - 26}[/tex]
Subtract 9 from 41
[tex]\frac{32}{6 * 3 - 26}[/tex]
Evaluate the denominator (Start by multiplying 6 * 3)
[tex]\frac{32}{18 - 26}[/tex]
[tex]\frac{32}{-8}[/tex]
Divide 32 by -8
-4
Hence;
[tex]\frac{41 - 3^2}{\sqrt{36} * 3 - 26} = -4[/tex]
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[tex]12 + 3\sqrt{8} * (9 - 2)[/tex]
Start by evaluating the bracket
[tex]12 + 3\sqrt{8} * 7[/tex]
Then evaluate the multiplication
[tex]12 + 21\sqrt{8}[/tex]
Simplify the square root
[tex]12 + 21\sqrt{4 * 2}[/tex]
Split the square root
[tex]12 + 21\sqrt{4} * \sqrt{2}[/tex]
Take Square root of 4
[tex]12 + 21 * 2} * \sqrt{2}[/tex]
[tex]12 + 42 \sqrt{2}[/tex]
Hence;
[tex]12 + 3\sqrt{8} * (9 - 2) = 12 + 42 \sqrt{2}[/tex]
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[tex]\frac{28 - (7^2 + 3)}{-13 + 3 * 5}[/tex]
Evaluate 7²
[tex]\frac{28 - (49 + 3)}{-13 + 3 * 5}[/tex]
Evaluate all expression in the bracket
[tex]\frac{28 - (52)}{-13 + 3 * 5}[/tex]
[tex]\frac{28 - 52}{-13 + 3 * 5}[/tex]
Evaluate 3 * 5
[tex]\frac{28 - 52}{-13 + 1 5}[/tex]
[tex]\frac{-2 4}{2}[/tex]
[tex]-12[/tex]
Hence;
[tex]\frac{28 - (7^2 + 3)}{-13 + 3 * 5} = -12[/tex]
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[tex]7^2 - 5* 8+1[/tex]
Evaluate 7²
[tex]49 - 5* 8+1[/tex]
Evaluate 5 * 8
[tex]49 - 40 + 1[/tex]
[tex]10[/tex]
[tex]7^2 - 5* 8+1 = 10[/tex]
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[tex](2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1[/tex]
Evaluate all square root and cube root
[tex](2 * 4) - (3 * 9) + 1[/tex]
Solve the expressions in bracket
[tex]8 - 27 + 1[/tex]
[tex]-18[/tex]
Hence;
[tex](2 * \sqrt{16}) - (\sqrt[3]{27} * \sqrt{81}) + 1 = -18[/tex]
