Question

Jaclyn estimates the square root of 50 in the following way:

Answer 1

Hello!

The answer is:

a) Her reasoning is incorrect, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.

b) We have that:

$\sqrt{200}=14.14$

and rounding to the nearest tenth, we have that:

$\sqrt{200}=14.1$

Why?

To solve the problem, we need to remember the following property of square roots:

$\sqrt{ab}=\sqrt{a}*\sqrt{b}$

We are given the expression:

$\sqrt{200}$

We can rewrite it by the following way:

$\sqrt{100*2}$

Now, applying the square root property we have:

$\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}=14.14$

Therefore,

a) Her reasoning was wrong, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.

b) We have that:

$\sqrt{200}=14.14$

and rounding to the nearest tenth, we have that:

$\sqrt{200}=14.1$

Have a nice day!