How do you simplify square root of three to the 15th power?

√(315)

1 Answer
George C.
Jan 27, 2018

√315=(√3)15=2187√3

Explanation:

The question is slightly ambiguous in that it could mean either of the following:

  • Take the square root of 3 then raise it to the 15th power, i.e. (√3)15

  • Raise 3 to the 15th power then take the square root, i.e. √315

In general if a≥0 then √a2b=a√b

So we find:

√315=√(37)2⋅3=37√3=2187√3

Also:

(√3)15=(√3)14√3=((√3)2)7⋅√3=37√3=2187√3

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