$\text{a)}$

$2\sqrt{3}=\sqrt{4}\cdot \sqrt{3}=\sqrt{12}$

$\sqrt{9}<\sqrt{12}<\sqrt{16}$

$3<\sqrt{12}<4$

---

$\text{b)}$

$3\sqrt{15}=\sqrt{9}\cdot \sqrt{15}=\sqrt{135}$

 

$\sqrt{121}<\sqrt{135}<\sqrt{144}$

$11<\sqrt{135}<12$

---

$\text{c)}$

$4\sqrt[3]{2}=\sqrt[3]{64}\cdot \sqrt[3]{2}=\sqrt[3]{128}$

 

$\sqrt[3]{125}<\sqrt[3]{128}<\sqrt[3]{216}$

$5<\sqrt[3]{128}<6$

---

$\text{d)}$

$3\sqrt[3]{10}=\sqrt[3]{27}\cdot \sqrt[3]{10}=\sqrt[3]{270}$

 

$\sqrt[3]{216}<\sqrt[3]{270}<\sqrt[3]{343}$

$6<\sqrt[3]{270}<7$