Question

1) So sánh:

a) \(2\) và \(\sqrt{5}\)

b) \(5\) và \(\sqrt{23}\)

c) \(\sqrt{23}+\sqrt{13}\) và \(\sqrt{83}\)

2) Tìm x:

a) \(\sqrt{x}=5\)

b) \(3\sqrt{x}=6\)

c) \(\sqrt{x}=5\)
d) \(3-\sqrt{3+1}=1\)

Answer 1

1. a)\(2\&\sqrt{5}\)

\(2=\sqrt{4}\)

=> \(2< \sqrt{5}\)

b)\(5\&\sqrt{23}\)

\(5=\sqrt{25}\)

=> \(5>\sqrt{23}\)

c) \(\sqrt{23}+\sqrt{13}\&\sqrt{83}\)

\(\left(\sqrt{23}+\sqrt{13}\right)^2=36+2\sqrt{229}\)

\(\left(\sqrt{83}\right)^2=83\)

\(\Rightarrow36+2\sqrt{299}< 83\)

=> \(\sqrt{23}+\sqrt{13}< \sqrt{83}\)

2. a) \(\sqrt{x}=5;x\ge0\)

=> x = 25

b) \(3\sqrt{x}=6;x\ge0\)

=> x = 4

c) trùng

d) \(3-\sqrt{3+1}=1\)

\(3-\sqrt{3+1}=3-2=1\)

Answer 2

1)

a)\(2=\sqrt{4}< \sqrt{5}\)

b) \(5=\sqrt{25}>\sqrt{23}\)

c) \(\sqrt{83}>\sqrt{81}=9\)

\(\left\{{}\begin{matrix}\sqrt{23}< \sqrt{25}=5\\\sqrt{13}< \sqrt{16}=4\end{matrix}\right.\)

\(\sqrt{23}+\sqrt{13}< 4+5=9\)

Vậy \(\sqrt{23}+\sqrt{13}< \sqrt{83}\)

2) Ta có:

\(\sqrt{x}=5\Rightarrow x=25\)

\(3\sqrt{x}=6\Rightarrow\sqrt{x}=2\Rightarrow x=4\)

\(3-\sqrt{3+1}=1\)

Nên:

\(3-2=1\)(luôn đúng)