Question

What values of x satisfy the equation x^2 =6? Please express your answer in exponent and radical form if necessary

Answer 1

x = ±6^(1/2)

x = ±√6

Explanation:

We know that even powers of odd numbers give the same result as even powers of even numbers. That is, x may be positive or negative. We can find the solutions by raising both sides of the equation to the 1/2 power.

(x^2)^(1/2) = 6^(1/2)

x = ±6^(1/2)

x = ±√6

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Additional comment

The rule of exponents that lets us simplify (x^2)^(1/2) is ...

(a^b)^c = a^(bc)

That means (x^2)^(1/2) = x^(2/2) = x^1 = x.

The denominator of a fractional exponent can be written as the index in a radical expression:

`x^(1/n)=\sqrt[n]{x}`