Get the solution to "To calculate: To simplify the expression 243−813."

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waigaK

Answered question

2021-10-23

To calculate:
To simplify the expression $\sqrt[3]{24} - \sqrt[3]{81}$ .

Answer & Explanation

2abehn

Skilled2021-10-24Added 88 answers

Calculation:
When two similar irrational numbers are added or subtracted, the rational parts of the two numbers are added or subtracted.
This can be written as:
$\sqrt[3]{24} - \sqrt[3]{81} = \sqrt{2 \times 2 \times 2 \times 3 \times x} - \sqrt[3]{3 \times 3 \times 3 \times 3 \times x}$
$\sqrt[3]{24} - \sqrt[3]{81} = \sqrt[3]{2^{3} \times 3 x} - \sqrt[3]{3^{3} \times 3 x}$
$\sqrt[3]{24} - \sqrt[3]{81} = \sqrt[3]{2^{3}} \sqrt[3]{3 x} - \sqrt[3]{3^{3}} \sqrt[3]{3 x}$ (Since the product rule for square root states that $\sqrt{a b} = \sqrt{a} \sqrt{b})$
$\sqrt[3]{24} - \sqrt[3]{81} = \sqrt[3]{2^{3}} \sqrt[3]{3 x} - \sqrt[3]{3^{3}} \sqrt[3]{3 x}$ (Since cube and cube root are opposite operations, they cancel out)
$\sqrt[3]{24} - \sqrt[3]{81} = 2 \sqrt[3]{3 x} = 3 \sqrt[3]{3 x}$
$\sqrt[3]{24} - \sqrt[3]{81} = (2 - 3) \sqrt[3]{3 x}$ .

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