Question

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

Answer 1

Answer:

$5\sqrt{3}$ OR $8.69$

Step-by-step explanation:

Let's first simplify $\sqrt{75}$.

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 $\sqrt{75}$ as:

$5\sqrt{3}$

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: $\frac{75}{8}=9.375$

Take the average of that answer and 8: $\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875$

This answer we got is extremely close to the exact answer of $\sqrt{75}$, which is $8.66025403...$. Since we are estimating, the answer above will do just fine.