Question

Find the simplification of \[\sqrt { - 9} \].

Answer 1

Hint:Every time we have a negative sign in the root, which means the solution is imaginary. Since the number inside the square root is negative so we have an imaginary solution. Imaginary is represented as \[i\]. Square root is a number which produces a specified quantity when multiplied by itself. It is a factor of a number that when squared gives the number the square root.

Complete step by step solution:
Negative numbers do not have real square roots since a square is either positive or zero. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they cannot be written as the quotient of two integers.
As we can see according to the question the number inside the square root is \[ - 9\], so the solution is imaginary.
\[i\]Or imaginary, equals to \[\sqrt { - 1} \], so we can take that out of the root.
Hence, we have
\[
\sqrt 9 \times \sqrt { - 1} \\
\Rightarrow 3 \times i \\
\Rightarrow 3i \\
\]
Hence the simplification of \[\sqrt { - 9} \] is \[3i\].

Note:All positive real numbers have 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 as 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 square root is written with a radical symbol \[\sqrt {} \] and the number or expression inside the radical symbol is called the radicand.