How do you simplify #root(3)(162)#?

Answer 1

#root(3)162=3root(3)6#

To simplify #root(3)162#, we should first factorize #162# into prime factors.

One way to calculate the factor of two is as

#162=2xx3xx3xx3xx3#

As we are taking out cube root of #162#, we should make group of three same numbers. In the given case, we can have it only one group of prime factor #3# and hence for cube root we can takeout only one #3#.

#root(3)162=root(3)(2xxul(3xx3xx3)xx3)#

or #root(3)162=3root(3)(2xx3)#

Hence #root(3)162=3root(3)6#

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Answer 2

Benjamin Altschul

To simplify (\sqrt[3]{162}), we first find the prime factorization of 162, which is (2 \times 3^4). Then, we group the factors in sets of three, as we are taking the cube root. This gives us (3 \times \sqrt[3]{2^3 \times 3^3}). Simplifying inside the cube root gives us (3 \times \sqrt[3]{8 \times 27}). Now, we can simplify further by taking the cube root of 8 (which is 2) and the cube root of 27 (which is 3). Multiplying these results gives us (3 \times 2 \times 3 = 18). Therefore, (\sqrt[3]{162} = 18).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.