What is the irrational cube root ^3√81 rewritten as a product of an integer and another irrational cube root?
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The irrational cube root ^3√81 can be rewritten as 3√(27) × 3√(81).
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The irrational cube root ^3√81 can be rewritten as ∛(3 × 27).
To rewrite the irrational cube root ^3√81 as a product of an integer and another irrational cube root, we need to figure out the prime factorization of 81.
First, we can find the prime factors of 81 by dividing it by the smallest prime number, which is 3:
81 ÷ 3 = 27
Now, we divide 27 by 3 again:
27 ÷ 3 = 9
Finally, we divide 9 by 3:
9 ÷ 3 = 3
Since 3 is prime, we stop here. The prime factorization of 81 is 3 × 3 × 3 × 3 or 3^4.
Now, let's rewrite ^3√81 as a product of an integer and another irrational cube root:
^3√81 = ^3√(3^4)
Since one factor of 3^4 is 3 (a perfect cube), we can rewrite ^3√81 as:
^3√81 = 3 × ^3√(3)
Therefore, the irrational cube root ^3√81 can be rewritten as the product of an integer (3) and another irrational cube root (^3√3).