Chapter 7 - Section 7.1 - Radicals and Radical Functions - Exercise Set - Page 418: 117

the value must be between $3$ and $4$

Work Step by Step

The value of $\sqrt{13}$ is definitely not equal to $5.7,$ because $5.7^2$ is greater than $5^2$ (which is equal to $25.$) This not close to $13.$ Also, the value of $\sqrt{13}$ is between the value of $\sqrt{9}$ and $\sqrt{16}$. So the value of $\sqrt{13}$ must be between $3$ and $4.$

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