Question

the value of cube root 24 + cube root 81 - cube root 192 is

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Concept:

Finding a number that, when multiplied twice by itself, equals the original number is necessary in order to compute the square root of any number. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to find the cube root of any number.

Given:

$&\sqrt[3]{24}+\sqrt[3]{81}-\sqrt[3]{192}$

Find:

$&\sqrt[3]{24}+\sqrt[3]{81}-\sqrt[3]{192}$

Solution:

We must ascertain which number was squared in order to arrive at the original number in order to calculate the number's square root. For instance, if we need to determine the root of 16, we already know that the result of multiplying 4 by 4 is 16. Hence, √16 = 4. Similar to this, it is simple to figure out that the cube of 4 equals 64 when we need to calculate the cube root of a number, like 64. Thus, 4 is the cube root of 64. However, we must apply the prime factorization approach when the numbers are really large in order to find the roots.

          $&\sqrt[3]{24}+\sqrt[3]{81}-\sqrt[3]{192}$

       $=\sqrt[3]{8 * 3}+\sqrt[3]{27 * 3}-\sqrt[3]{64 * 3}\\\\=\sqrt[3]{2^{3} * 3}+\sqrt[3]{3^{3} * 3}-\sqrt[3]{4^{3} * 3} \\\\&=2 \sqrt[3]{3}+3 \sqrt[3]{3}-4 \sqrt[3]{3}\\\\=\sqrt[3]{3}$

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