Question

What is the order of √5 , -0.1, -5/3 , 0.7, √2from least to greatest?​

Answer 1

`\large\boxed{-(5)/(3),\ -0.1,\ 0.7,\ \sqrt2,\ \sqrt5}`

Explanation:

`\sqrt5\\\\-0.1=-√(0.1^2)=-√(0.01)\\\\-(5)/(3)=-\sqrt{\left((5)/(3)\right)^2}=-\sqrt{(25)/(9)}=-\sqrt{2(7)/(9)}\\\\0.7=√(0.7^2)=√(0.49)\\\\\sqrt2\\\\-\sqrt{2(7)/(9)}<-√(0.01)<√(0.49)<\sqrt2<\sqrt5`

Answer 2

-5/3, -0.1, 0.7, √2 and √5

Explanation:

To start ordering these items, we first need to have a common point of comparison... so we'll get an approximation of their decimal value. No need to be very precise, just have a rough estimate:

√5: roughly 2.2

-0.1: -0.1

-5/3: -1.66

0.7: 0.7

√2: roughly 1.4

Now that we have the same comparing point (a decimal value), it's easy to sort them from the smallest value to the greatest value:

-5/3, -0.1, 0.7, √2 and √5

Of course, √2 is smaller than √5