Solve Square Root of x⁴: Complete Step-by-Step Guide

Remember that square root asks "what squared gives this?" Since $(x^2)^2 = x^4$, the answer is $x^2$, not x!

Yes! That's exactly what happens when you use the rule properly. $\sqrt{x^4} = (x^4)^{\frac{1}{2}} = x^{4 \cdot \frac{1}{2}} = x^2$. Dividing 4 by 2 gives us the exponent 2.

For this algebraic simplification, we assume x can be any real number. The expression $\sqrt{x^4}$ always equals $x^2$ because any number squared is positive.

Think of it as "powers multiply when raising a power to a power." So $(x^4)^{\frac{1}{2}}$ becomes $x^{4 \times \frac{1}{2}} = x^2$.

Converting to fractional exponents lets us use the power rules consistently. It's much easier to multiply exponents than to work with radical symbols directly.