Question

Cравнение 1/2√8 и 1/5√100

Answer 1

1/2√8 ? 1/5√100
(1/2√8)^2 ? (1/5√100)^2
1/4×8 ? 1/25×100
0,25×8 ? 0,04×100
2 < 4
1/2√8 < 1/5√100

Answer 2

To compare 1/2√8 and 1/5√100, we can simplify each expression and then compare them.

First, let's simplify 1/2√8:

1/2√8 = 1/2 * √(1/8) = 1/2 * √(1/4 * 1/2) = 1/2 * √1/4 * √1/2 = 1/2 * 1/2 * √1/2 = 1/4√2

Now let's simplify 1/5√100:

1/5√100 = 1/5 * √(1/100) = 1/5 * √1/4 = 1/5 * 1/2 = 1/10

So we have 1/4√2 and 1/10.

To compare them, we can convert both fractions to have a common denominator:

1/4√2 = 1/4√2 * √2/√2 = √2/8

So we have √2/8 and 1/10.

To compare these, we can convert them to decimals:

√2/8 ≈ 0.1768

1/10 = 0.1

Since 0.1768 is greater than 0.1, we can conclude that 1/2√8 is greater than 1/5√100.