Question

Simplify the irrational number 75; then estimate it to two decimal places.

Answer 1

`5√(3)` OR
`8.69`

Explanation:

Let's first simplify
`√(75)`.

5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write
`√(75)` as:

`5√(3)`

Now, let's find the answer in decimal form. We know that:

`8^2=64` and
`9^2=81`

With that information, we know that the answer has to be between 8 and 9.

Divide 75 by 8:
`(75)/(8)=9.375`

Take the average of that answer and 8:
`(9.375+8)/(2)=(17.375)/(2)=8.6875`

This answer we got is extremely close to the exact answer of
`√(75)`, which is
`8.66025403...`. Since we are estimating, the answer above will do just fine.