Rewrite the radical expression as an exponential expression: $\sqrt{3-y^2}$

Expert intro: A square root can always be rewritten using exponent notation with power $1/2$.

Detailed walkthrough

Use the rule

$\sqrt{a}=a^{\frac{1}{2}}$

So

$\sqrt{3-y^2}=(3-y^2)^{\frac{1}{2}}$

That is the exponential expression.

💡 Pitfall guide

Be careful not to distribute the exponent across subtraction. The expression is $(3-y^2)^{1/2}$, not $3^{1/2}-y$ or 3^{1/2}-y^2^{1/2}.

🔄 Real-world variant

If the expression were $\sqrt[4]{3-y^2}$, then it would become $(3-y^2)^{1/4}$.

🔍 Related terms

square root, radical form, exponential notation