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

1 Answer
Shwetank Mauria
May 10, 2016

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

Explanation:

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

The factor of two can be worked out 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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