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a) \(6=\sqrt[3]{6^3}=\sqrt{216}>\sqrt[3]{208}=2\sqrt[3]{26}\)

b) \(2\sqrt[3]{6}=\sqrt[3]{2^3.6}=\sqrt[3]{48}>\sqrt[3]{47}\)

Dễ mà:vvv

Ta có: \(\left\{{}\begin{matrix}\sqrt{37}>\sqrt{36}=6\\\sqrt{26}>\sqrt{25}=5\end{matrix}\right.\)

=> \(\sqrt{37}+\sqrt{26}+1>\sqrt{36}+\sqrt{25}+1=6+5+1=12\)

Mà \(\sqrt{144}=12\)

=> \(\sqrt{37}+\sqrt{26}+1>\sqrt{144}\)

Ta có: \(\sqrt{37}>\sqrt{36}=6\)

\(\sqrt{26}>\sqrt{25}=5\)

Do đó: \(\sqrt{37}+\sqrt{26}>6+5=11\)

\(\Leftrightarrow\sqrt{37}+\sqrt{26}+1>12\)

hay \(\sqrt{144}< \sqrt{37}+\sqrt{26}+1\)

Ta có \(\sqrt{144}\)=12=6+5+1=\(\sqrt{36}+\sqrt{25}+\sqrt{1}\)

   Vì 0<25<26=>\(\sqrt{25}< \sqrt{26}\)(1)

    Vì 0<36<37=>\(\sqrt{36}< \sqrt{37}\)(2)

Từ (1) và (2), ta có \(\sqrt{36}+\sqrt{25}< \sqrt{37}+\sqrt{26}\)

=>\(\sqrt{36}+\sqrt{25}+\sqrt{1}< \sqrt{37}+\sqrt{26}+\sqrt{1}\)

Hay 12<\(\sqrt{37}+\sqrt{26}+1\)

Hay\(\sqrt{144}\)<\(\sqrt{37}+\sqrt{26}+1\)

\(\left(\sqrt{24}+\sqrt{26}\right)^2=50+8\sqrt{39}\)

\(10^2=100=50+50\)

mà \(8\sqrt{39}< 50\)

nên \(\sqrt{24}+\sqrt{26}< 10\)

Giúp mình với mn

\(\sqrt{3}+\sqrt{15}< \sqrt{5}+\sqrt{16}=\sqrt{5}+4\)

Ta có:

\(\sqrt[3]{7}< \sqrt[3]{8}=2\) và \(\sqrt{15}< \sqrt{16}=4\), suy ra \(\sqrt[3]{7}+\sqrt{15}< 6\).

\(\sqrt{10}>\sqrt{9}=3\) và \(\sqrt[3]{28}>\sqrt[3]{27}=3\), suy ra \(\sqrt{10}+\sqrt[3]{28}>6\).

Vậy \(\sqrt[3]{7}+\sqrt{15}< \sqrt{10}+\sqrt[3]{28}\).