Does a square root have two values?

Before finding does a square root has two values we must first know what are squares, square roots and others.

What is a Square?

Square of a number is defined as the value obtained by the multiplication of the number by itself. The exponential form of a square of a number x is written as x².

For eg: Square of 2 is 2² = 2 × 2 = 4.

Square of a negative number is also a positive number. For eg: Square of -2 is (-2)² = -2 × -2 = 4.

From the above two examples, it can be seen that the square of positive and negative numbers is always positive.

What is a Square Root?

Square Root of a number is the inverse operation of the square. If the square root of a number x is y, then the square of y is x. The exponential form of the square root is written as x^-2. The square root of the number x is represented as √x.

For eg: Square Root of 25 is √25 = √(5²) = 5.

Does a Square Root have Two Values?

Solution:

Square root of a number always has two answers, one is positive and one is negative. There are two answers because the square of a negative and positive number is the same.

For eg: Square of 3 is 9 and the square of -3 is also 9. So the square root of 9 is 3 and -3. Similarly, the square root of a number y is x and -x.

Similar Questions

Question 1: Calculate the square root of 36?

Solution:

Given number is 36

Write prime factors of 36

36 = 2 × 2 × 3 × 3

36 = 2² × 3³

Now calculate the square root of the numbers.

√36 = √(2² × 3²)

√36 = ±(2 × 3) = ±6

Hence, square root of the given number is 6 and -6

Question 2: Calculate the square root of 144?

Solution:

Given number is 144

Write prime factors of 144

144 = 2 × 2 × 2 × 2 × 3 × 3

144 = 2⁴ × 3²

Now calculate square root of numbers

√144 = √(2⁴ × 3²)

√144 = ±(4 × 3) = ±12

Hence, square root of the given number is 12 and -12