-1 có căn k bạn?

39 < 103

1 + căn 15 ......căn 24

4.872983346...\(\approx\) 4.872    và 4.898979486...\(\approx\)4.898

=> 4.872 < 4.898

=> 1 + căn 15 < căn 24

1/

Ta có:  \(\left(1+\sqrt{15}\right)^2\)= 1 + 15 + \(2\sqrt{15}\)= 16 + \(2\sqrt{15}\)

              \(\sqrt{24}^2\)= 24 = 16 + 8

Vì:     \(\sqrt{15}^2\)= 15 < 16 =\(4^2\)

Nên:   \(\sqrt{15}< 4\)

=>       \(2\sqrt{15}< 8\)

=>       \(16+2\sqrt{15}< 24\)

=>      \(\left(1+\sqrt{15}\right)^2< \sqrt{24}^2\)

Vậy     \(1+\sqrt{15}< \sqrt{24}\)

2/

b/    \(3x-7\sqrt{x}=20\)\(\left(x\ge0\right)\)

<=> \(3x-7\sqrt{x}-20=0\)

<=> \(3x-12\sqrt{x}+5\sqrt{x}-20=0\)

<=> \(3\sqrt{x}\left(\sqrt{x}-4\right)+5\left(\sqrt{x}-4\right)=0\)

<=> \(\left(\sqrt{x}-4\right)\left(3\sqrt{x}+5\right)=0\)

<=> \(\sqrt{x}-4=0\)hoặc \(3\sqrt{x}+5=0\)

<=>   \(\sqrt{x}=4\)hoặc \(3\sqrt{x}=-5\)(vô nghiệm)

<=>   \(x=16\)

Vậy S=\(\left\{16\right\}\)

c/    \(1+\sqrt{3x}>3\)

<=> \(\sqrt{3x}>2\)

<=>   \(3x>4\)

<=>  \(x>\frac{4}{3}\)

d/      \(x^2-x\sqrt{x}-5x-\sqrt{x}-6=0\)(\(x\ge0\))

<=>   \(\left(x^2-5x-6\right)-\left(x\sqrt{x}+\sqrt{x}\right)=0\)

<=>   \(\left(x^2-6x+x-6\right)-\left(x\sqrt{x}+\sqrt{x}\right)=0\)

<=>    \([x\left(x-6\right)+\left(x-6\right)]-\sqrt{x}\left(x+1\right)=0\)

<=>   \(\left(x-6\right)\left(x+1\right)-\sqrt{x}\left(x+1\right)=0\)

<=>   \(\left(x+1\right)\left(x-6-\sqrt{x}\right)=0\)

<=>    \(\left(x+1\right)\left(x-3\sqrt{x}+2\sqrt{x}-6\right)=0\) 

<=>    \(\left(x+1\right)[\sqrt{x}\left(\sqrt{x}-3\right)+2\left(\sqrt{x}-3\right)]=0\)

<=>    \(\left(x+1\right)\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)=0\)

<=>     \(x+1=0\)  hoặc \(\sqrt{x}-3=0\)hoặc \(\sqrt{x}+2=0\)

<=>     \(x=-1\)(loại)  hoặc \(x=9\)hoặc \(\sqrt{x}=-2\)(vô nghiệm)

Vậy S={  9 }

a) \(5+\sqrt{47}\) và \(\sqrt{40}+\sqrt{23}\)

Ta có: \(5+\sqrt{47}=\sqrt{25}+\sqrt{47}\)

Vì \(\sqrt{25}+\sqrt{47}>\sqrt{40}+\sqrt{23}\)

\(\Rightarrow5+\sqrt{47}>\sqrt{40}+\sqrt{23}\)

b) Ta có: 14=5+9=\(\sqrt{25}+\sqrt{81}\)

Vì \(\sqrt{24}+\sqrt{80}< \)\(\sqrt{25}+\sqrt{81}\)

\(\Rightarrow\)\(\sqrt{24}+\sqrt{80}< \)14

c) Ta có: \(15=9+6=\sqrt{81}+\sqrt{36}\)

Vì \(\sqrt{62}+\sqrt{35}< \)\(\sqrt{81}+\sqrt{36}\)

\(\Rightarrow\sqrt{62}+\sqrt{35}< 15\)

a) Ta có: 
√2005 + √2003 > √2002 + √2000 
<=> 1/(√2005 + √2003) < 1/(√2002 + √2000) 
<=> 2/(√2005 + √2003) < 2/(√2002 + √2000) 
<=> (2005 - 2003)/(√2005 + √2003) < (2002 - 2000)/(√2002 + √2000) 
<=> √2005 - √2003 < √2002 - √2000 
<=> √2005 + √2000 < √2002 + √2003 

b) Tương tự câu a 
√(a + 6) + √(a + 4) > √(a + 2) + √a 
<=> 1/[√(a + 6) + √(a + 4)] < 1/[√(a + 2) + √a] 
<=> 2/[√(a + 6) + √(a + 4)] < 2/[√(a + 2) + √a] 
<=> [(a + 6) - (a + 4)/[√(a + 6) + √(a + 4)] < [(a + 2) - a]/[√(a + 2) + √a] 
<=> √(a + 6) - √(a + 4) < √(a + 2) - √a 
<=> √(a + 6) + √a < √(a + 4) + √(a + 2) 

hình như nó sai cái gì a

\(8=\sqrt{64}\)

vì 64>63

8>căn 63

\(13=\sqrt{169}\)

vì 170>169

căn 170 > 13

\(15=\sqrt{225}\)

vì 225<227

15 < căn 227

\(\sqrt{15}-1< \sqrt{16}-1=3\)

\(3< \sqrt{10}\)

Do đó: \(\sqrt{15}-1< \sqrt{10}\)

\(\sqrt{235}\)=15,32970972

=>15<\(\sqrt{235}\)