Dealing v the concerns of attributes in eleventh course my gimpppa.orgs teacher claims that square root of a genuine number is constantly positive. Just how is the possible?  Given a optimistic real number \$a\$, there space two options to the equation \$x^2 = a\$, one is positive, and the various other is negative. We signify the positive root (which us often call the square root) by \$sqrta\$. The an unfavorable solution of \$x^2 = a\$ is \$-sqrta\$ (we understand that if \$x\$ satisfies \$x^2 = a\$, then \$(-x)^2 = x^2 = a\$, therefore, due to the fact that \$sqrta\$ is a solution, for this reason is \$-sqrta\$). So, because that \$a > 0\$, \$sqrta > 0\$, however there are two options to the equation \$x^2 = a\$, one hopeful (\$sqrta\$) and also one an adverse (\$-sqrta\$). For \$a = 0\$, the two solutions coincide through \$sqrt0 = 0\$.

You are watching: Positive numbers have negative square roots true or false

re-publishing
point out
monitor
answered may 26 "14 in ~ 1:01 Michael AlbaneseMichael Albanese
\$endgroup\$
6
| show 1 an ext comment
7
\$egingroup\$
It is just a notational matter. Through convention, for optimistic \$x\$ (real clearly), \$sqrtx\$ denotes the positive square root of the genuine number \$x\$. Similarly we agree by way of notational convention that \$-sqrtx\$ is the an unfavorable square root of \$x\$. The course, every confident real number, \$x\$, has two square roots, \$sqrtx\$ and \$-sqrtx\$, hopeful and an unfavorable real number respectively.

I problem sometimes about what gets taught by way gimpppa.orgematics in an additional school these days.

re-superstructure
mention
monitor
edited might 26 "14 in ~ 7:02 usergimpppa.org
answered might 26 "14 in ~ 6:34 Richard GayleRichard Gayle
\$endgroup\$
1
2
\$egingroup\$
Technically this explain is wrong. He might say, "The square root of a positive number is hopeful (by definition)". E.g. For 0 you get \$sqrt0=0\$ which is neither optimistic nor negative. And also for negative numbers you also get complex solutions which are neither positive nor an adverse nor 0.

The identify article and the singular in "the square root" is additionally important to indicate the conventional meaning of \$sqrt\$. But much more correctly he must say "the major square root", since gimpppa.orgematically the expression "the square root" doesn"t do sense, due to the fact that there are two different roots in general.

re-superstructure
cite
follow
answered may 26 "14 in ~ 18:18
David OngaroDavid Ongaro
\$endgroup\$