Question

Bài 1: so sánh

a) \(2^{300}\) và \(3^{200}\)

b) \(\dfrac{13}{38}\) và \(\dfrac{1}{3}\)

c) \(\sqrt{235}\) và 15

Answer 1

a) \(2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

Do : \(8^{100}< 9^{100}\)

=> \(2^{300}< 3^{200}\)

b) Do \(\dfrac{13}{38}>\dfrac{13}{39}\)

Mà : \(\dfrac{13}{39}=\dfrac{1}{3}\)

=> \(\dfrac{13}{38}>\dfrac{1}{3}\)

c)Do : \(\sqrt{235}>\sqrt{225}\)

Mà : \(\sqrt{225}=15\)

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

Answer 2

a) Ta có:

\(2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

Ta thấy 8<9 suy ra \(8^{100}< 9^{100}\)

Vậy \(2^{300}< 3^{200}\)

Answer 3

b) Ta có:

38<39 suy ra \(\dfrac{13}{38}>\dfrac{13}{39}=\dfrac{1}{3}\)

suy ra \(\dfrac{13}{38}>\dfrac{1}{3}\)

Answer 4

\(\sqrt{235}>\sqrt{225}=15\)

suy ra \(\sqrt{235}>15\)

Answer 5

a, 2³⁰⁰ =(2³)¹⁰⁰ =8¹⁰⁰

3²⁰⁰ =(3²)¹⁰⁰=9¹⁰⁰

vậy 8¹⁰⁰<9¹⁰⁰ hay 2³⁰⁰<3²⁰⁰

Answer 6

Bài 1: So sánh

a) 2\(^{300}\)= (2\(^3\))\(^{100}\)=8\(^{100}\)

3\(^{200}\)=(3\(^2\))\(^{100}\)= 9\(^{100}\)

Vì 8<9; 100>0 nên => 8\(^{100}\)<9\(^{100}\)

b) Do \(\frac{13}{38}\)>\(\frac{13}{39}\)

Mà \(\frac{13}{39}\)=\(\frac{1}{3}\)

=> \(\frac{13}{38}\)>\(\frac{1}{3}\)

c) Do \(\sqrt{235}\)>\(\sqrt{225}\)

Mà \(\sqrt{225}\)= 15

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

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