A girl puts the number 6 on the display of her calculator, presses the square root button, multiplies the answer by 2 and then squares that answer.Her calculator would be showing:
With the calculator on this site, if you press = after each stage you get the following:
On the other hand, if you use brackets at each stage and don't press = until the very end you get:
The small inaccuracy in the first arises because √6 is an irrational number and the calculator only stores it to a finite precision.
Why don't we do it on the site calculator and see what happens
A girl puts the number 6 on the display of her calculator, presses the square root button, multiplies the answer by 2 and then squares that answer.Her calculator would be showing:
This is without hitting the equal sign.
sqrt 6 * 2 ^2
$${\sqrt{{\mathtt{6}}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{2}}} = {\mathtt{9.797\: \!958\: \!971\: \!132\: \!712\: \!4}}$$
Below is the answer if you do hit the equal sign as you go through.
6 sqrt = * 2 = ^2
$${\mathtt{sqrt6}}{\mathtt{\,\times\,}}{\mathtt{2}} = {\sqrt{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\mathtt{2}}$$
$${\left({\mathtt{sqrt6}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{{\mathtt{2}}} = {{\left({\sqrt{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}}^{{\mathtt{2}}}$$= 24
sqrt6 on this calculator is often entered as 6 sqrt on older calculators.
So it the equal sign is hit as you go through the question. Because it does so
(1)multiply the answer
(2)square that answer
The only way you can get a running 'answer' like this is to keep hitting the equal sign.
With the calculator on this site, if you press = after each stage you get the following:
On the other hand, if you use brackets at each stage and don't press = until the very end you get:
The small inaccuracy in the first arises because √6 is an irrational number and the calculator only stores it to a finite precision.