Question

So sánh \(\sqrt{144}\) và \(\sqrt{37}\)+\(\sqrt{26}\)+1

Answer 1

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 \(\sqrt{144}=12\)

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

Answer 2

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

Answer 3

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