\(\sqrt{27}-\sqrt{12}-\sqrt{2016}>\sqrt{25}-\sqrt{16}-\sqrt{2025}\)

\(=5-4-45=-44\)

Vậy \(\sqrt{27}-\sqrt{12}-\sqrt{2016}>-44\)

Có : \(\sqrt{12}< \sqrt{16}=4\)

         \(\sqrt{2016}< \sqrt{2025}\)         => \(\sqrt{12}+\sqrt{2016}< 4+45\)

                                                                 => \(-\sqrt{12}-\sqrt{2016}>-49\)(1)

Lại có : \(\sqrt{27}>\sqrt{25}=5\)(2)

Từ (1),(2) có : \(\sqrt{27}-\sqrt{12}-\sqrt{2016}>5-49\)or \(\sqrt{27}-\sqrt{12}-\sqrt{2016}>-44\)

\(\sqrt{27}-\sqrt{12}-\sqrt{2016}>\)-44

\(\sqrt{2017}-\sqrt{2016}=\dfrac{1}{\sqrt{2017}+\sqrt{2016}}\)

\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)

2017>2015

=>căn 2017>căn 2015

=>\(\sqrt{2017}+\sqrt{2016}>\sqrt{2016}+\sqrt{2015}\)

=>\(\dfrac{1}{\sqrt{2017}+\sqrt{2016}}< \dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)

=>\(\sqrt{2017}-\sqrt{2016}< \sqrt{2016}-\sqrt{2015}\)

\(\frac{2016}{\sqrt{2016}}=\sqrt{2016}\)

\(\frac{2017}{\sqrt{2017}}=\sqrt{2017}\)

=> Bằng nhau

\(\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}-\sqrt{2016}-\sqrt{2017}=\left(\frac{2016}{\sqrt{2017}}-\sqrt{2017}\right)+\left(\frac{2017}{\sqrt{2016}}-\sqrt{2016}\right)\)

\(=\frac{2016-2017}{\sqrt{2017}}+\frac{2017-2016}{\sqrt{2016}}=\frac{1}{\sqrt{2016}}-\frac{1}{\sqrt{2017}}\)

vì \(2016< 2017\Rightarrow\sqrt{2016}< \sqrt{2017}\Rightarrow\frac{1}{\sqrt{2016}}>\frac{1}{\sqrt{2017}}\Rightarrow\frac{1}{\sqrt{2016}}-\frac{1}{\sqrt{2017}}>0\)

\(\Rightarrow\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}-\sqrt{2016}-\sqrt{2017}>0\Rightarrow\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}>\sqrt{2016}+\sqrt{2017}\)

tick đi sau làm cho

t

Big hero 6 đáp án là > mà 

Không biết !

A  <  20

học tốt

Ta thấy :

\(A=\sqrt{12}+\sqrt{20}+\sqrt{30}+\sqrt{42}< \sqrt{12,25}+\sqrt{20,25}+\sqrt{30,25}+\sqrt{42,25}=20\)

\(\Rightarrow A< 20\)

Vậy A < 20

~Study well~

#KSJ

Ta có:

\(\sqrt{2016}-\sqrt{2017}=\frac{\left(\sqrt{2016}-\sqrt{2017}\right)\left(\sqrt{2016}+\sqrt{2017}\right)}{\sqrt{2016}+\sqrt{2017}}\)

\(=\frac{2016-2017}{\sqrt{2016}+\sqrt{2017}}=-\frac{1}{\sqrt{2016}+\sqrt{2017}}\)

\(\sqrt{2017}-\sqrt{2018}=\frac{\left(\sqrt{2017}-\sqrt{2018}\right)\left(\sqrt{2017}+\sqrt{2018}\right)}{\sqrt{2017}+\sqrt{2018}}\)

\(=\frac{2017-2018}{\sqrt{2017}+\sqrt{2018}}=-\frac{1}{\sqrt{2017}+\sqrt{2018}}\)

Ta thấy rằng:

\(\sqrt{2018}>\sqrt{2016}\)

\(\Leftrightarrow\sqrt{2017}+\sqrt{2018}>\sqrt{2016}+\sqrt{2017}\)

\(\Leftrightarrow\frac{1}{\sqrt{2017}+\sqrt{2018}}< \frac{1}{\sqrt{2016}+\sqrt{2017}}\)

\(\Leftrightarrow-\frac{1}{\sqrt{2017}+\sqrt{2018}}>-\frac{1}{\sqrt{2016}+\sqrt{2017}}\)

Vậy \(\sqrt{2017}-\sqrt{2018}>\sqrt{2016}-\sqrt{2017}\)

bawngf nhau

giải ra giùm mình với bạn -.-

b: \(\sqrt{2017}-\sqrt{2016}=\dfrac{1}{\sqrt{2016}+\sqrt{2017}}\)

\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)

mà \(\sqrt{2016}+\sqrt{2017}< \sqrt{2016}+\sqrt{2015}\)

nên \(\sqrt{2017}-\sqrt{2016}>\sqrt{2016}-\sqrt{2015}\)

a) Có \(\sqrt{2}< \sqrt{2,25}=1,5\)

\(\sqrt{6}< \sqrt{6,25}=2,5\); 

\(\sqrt{12}< \sqrt{12,25}=3,5\); 

\(\sqrt{20}< \sqrt{20,25}=4,5\)

=> \(P=\sqrt{2}+\sqrt{6}+\sqrt{12}+\sqrt{20}< 1,5+2,5+3,5+4,5=12\)

Vậy P < 12

Answer:

ý a, tham khảo bài làm của @xyzquynhdi

\(\sqrt{2}+\sqrt{3}+\sqrt{5}\)

\(\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}\)

\(=\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)

\(=\sqrt{\left(\sqrt{2}\right)^2+\left(\sqrt{3}\right)^2+\left(\sqrt{5}\right)^2+2\sqrt{2}\sqrt{3}+2\sqrt{2}\sqrt{5}+2\sqrt{3}\sqrt{5}}\)

\(=\sqrt{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)^2}=\sqrt{2}+\sqrt{3}+\sqrt{5}\)