which sign makes the statement true? -\\sqrt3{63} ? -\\sqrt{23}

Explanation:

Step1: Approximate cube - root value

We know that $4^3=64$ and $3^3 = 27$. So, $\sqrt[3]{63}$ is close to 4. Then $-\sqrt[3]{63}\approx - 4$.

Step2: Approximate square - root value

We know that $4^2 = 16$ and $5^2=25$. So, $\sqrt{23}$ is between 4 and 5, closer to 5. Then $-\sqrt{23}\approx - 5$.

Step3: Compare the two values

Since $-4>-5$, we have $-\sqrt[3]{63}>-\sqrt{23}$.

Answer:

$>$