If squaring a number means multiplying that number with itself climate shouldn"t acquisition square root of a number mean to division a number through itself?

For example the square the \$2\$ is \$2^2=2 cdot 2=4 \$ .

You are watching: A number that produces another number its square when multiplied by itself

But square source of \$2\$ is no \$frac22=1\$ . taking square root way reversing the impact of squaring. Dividing a number by itself does not do that (but rather always returns 1 as you noted).

Compare your question to: if doubling a number method adding it come itself, shouldn"t halving a number mean subtracting the from itself? Answer: clear not. Squaring when explained in basic English, provides the native "itself". Below is an effort to specify the reverse process, recognize square root, using words "itself":

The square root of a number \$N\$ is that number \$x\$ together that as soon as \$N\$ is separated by \$x\$ it offers itself (my grammar is poor, subject and object the this sentence. Yet I hope you gain the drift)

Edit: this idea translated to one equation would offer the following:if \$N = 9\$ then \$x = 3\$ and also \$N/x = 9\$?? ns guess chin in this context describes \$x\$ and not \$N\$

re-superstructure
mention
follow
edited january 15 "16 in ~ 15:06 msafi
311 bronze argorial
answered jan 9 "16 in ~ 6:43 p VanchinathanP Vanchinathan
\$endgroup\$
4
include a comment |
44
\$egingroup\$
Since this concern hinges directly on some basic ideas the charline-picon.com, this prize attempts come explicate those ideas in a similarly an essential way.

See more: How To Write The Formula For Lithium Acetate Formula Ionic Or Covalent

Squaring a number can be assumed of as a procedure.The details procedure for squaring a number can use atemplate choose the following:

\$\$ Box longrightarrow Box imesBox longrightarrow Box \$\$

We put the "input" value, for example, \$2\$, in the leftmost box, choose this:

\$\$ 2 longrightarrow Box imesBox longrightarrow Box \$\$

Next we make copies of the leftmost box and also put lock in the twoboxes in the middle:

\$\$ 2 longrightarrow 2 imes 2 longrightarrow Box \$\$

Notice that these 2 boxes must every contain the same number.Finally, we carry out the shown multiplication and also write the resultin the last crate on the right:

\$\$ 2 longrightarrow 2 imes 2 longrightarrow 4 \$\$

To take it a square root, we want to reverse the procedure, the is,work the backwards. So us take the "input" number, because that example, \$9\$,and placed it in package on the right:

\$\$ Box longrightarrow Box imesBox longrightarrow 9 \$\$

Now we have to decide what to placed in the two boxes in the middle.We understand we need the materials of the two boxes to it is in equal, and we knowthat as soon as we perform the multiplication the result has to be \$9\$.Suppose we guess the number in each box need to be \$3\$. Then we have:

\$\$ Box longrightarrow 3 imes3 longrightarrow 9 \$\$

We have the right to confirm that \$3 imes3\$ go indeed offer the an outcome \$9\$, therefore allis great so far. Currently we just need come deduce what number was in theleftmost box. We understand the middle boxes were filled through copying the box,so it had actually to save on computer a \$3\$ as well. So us have

\$\$ 3 longrightarrow 3 imes3 longrightarrow 9 \$\$

And that"s why the square root of \$9\$ is \$3\$ quite than \$9/9\$.(Well, that and also the fact that we refuse to placed \$-3\$ in the 2 boxes inthe middle, due to the fact that life is much better when we repetitively follow a rulethat says a "square root" should never it is in a an adverse number.)

We may later on learn exactly how to discover square root in a method that does notrely so lot on make a happy guess. However that"s a issue of analgorithm for calculating a square root, no the definition that a square root.