How do you solve 3√x2=9?

2 Answers
Dahlia S. · Stefan V.
Mar 30, 2017

Undo each of the things done to x one at a time.

Explanation:

First, to undo the cube root, we can cube both sides to get

x2=729

Next, to undo the square, we can take the square root of both sides to get

x=±27

George C.
Mar 30, 2017

x=±27

Explanation:

Given:

3√x2=9

Note that 9=32, so this can also be written:

3√x2=32

Note that both t→t3 and its inverse t→3√t are one to one as functions of real numbers. So if we cube both sides of the equation then we neither lose any solution nor introduce any extraneous solutions:

Cubing both sides of the equation, we get:

x2=(32)3=32⋅3=33⋅2=(33)2=272

Subtract 272 from both ends to get:

x2−272=0

The difference of squares identity can be written:

a2−b2=(a−b)(a+b)

Using this with a=x and b=27 we find:

0=x2−272=(x−27)(x+27)

So:

x=±27

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