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help me pleaseeeeeeeeeeFor the drop box we havethe result is (rational/irrational)because it (cannot/can)be written as the ratio of two integers and it’s decimal expansion (does/does not) terminate or repeat.

help me pleaseeeeeeeeeeFor the drop box we havethe result is (rational/irrational)because it (cannot/can)be written as the ratio of two integers and it’s decima class=

Answer :

Solution

We want to add

[tex]3\sqrt[]{2}+\sqrt[]{10}[/tex]

Solution

We will notice the like terms and then factorise

[tex]\begin{gathered} 3\sqrt[]{2}+\sqrt[]{10} \\ =3\sqrt[]{2}+\sqrt[]{5\times2} \\ =3\sqrt[]{2}+\sqrt[]{5}(\sqrt[]{2}) \\ =(3+\sqrt[]{5})\sqrt[]{2} \end{gathered}[/tex]

Therefore,

[tex]\operatorname{Re}sult=(3+\sqrt[]{5})\sqrt[]{2}[/tex]

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