Whats the square root of - 63 using radicand?

32 = 3⋅3=9 32 = 3⋅3=9

9 was the square of 3. The square of - 3 is 9 as well

(-3) 2 = (-3) ⋅ (-3) = 9 (-3) 2 = (-3) ⋅ (-3) = 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

a2 = a⋅a = (-a) ⋅ (-a) a2 = a⋅a = (-a) ⋅ (-a)

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.

a√ a

To indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root.

± 9√ = ±3 ±9=±3

Zero has one square root which is 0.

0√ = 0

Remember

√ (mn) = (√m) (√n)

so

√-63 = (√-1) (√63)

63=3*3*7

√63=3√7

√-63 = (3) (√7) (√-1)

√-63 = (3) (√-7)

√-63=3√-7