Square roots (Algebra 1 | square root symbol
InthefirstsectionofAlgebra1welearnedthat$$3{2}=3cdot3=9$$Wesaidthat9wasthesquareof3.Thesquareof-3is9aswell$$left(-3ight){2}=left(-3ight)cdotleft(-3ight)=9$$3and-3aresaidtobethesquarerootsof9.Allpositiverealnumbershastwosquareroots,onepositivesquarerootandonenegativesquareroot.Thepositivesquarerootissometimesreferredtoastheprincipalsquareroot.Thereasonthatwehavetwosquarerootsisexemplifiedabove.Theproductoftwonumbersispositiveifbothnumbershavethesamesignasisthecasewithsquaresandsquareroots$$a{...
In the first section of Algebra 1 we learned that
$$3{2}=3cdot 3=9$$
We said that 9 was the square of 3. The square of -3 is 9 as well
$$left (-3 ight ){2}=left (-3 ight )cdot left (-3 ight )=9$$
3 and -3 are said to be the square roots of 9.
All positive real numbers has two square roots, one positive square root and one negative square root. The positive square root is sometimes referred to as the principal square root. The reason that we have two square roots is exemplified above. The product of two numbers is positive if both numbers have the same sign as is the case with squares and square roots
$$a{2}=acdot a=left ( -a ight )cdot left ( -a ight )$$
A square root is written with a radical symbol √ and the number or expression inside the radical symbol, below denoted a, is called the radicand.
$$sqrt{a}$$
To indicate that we want both the positive and the negative square root of a radicand we ...