Like every other number, you can also find integer's square root but sometimes it can become complex. If you know how to find the square root of any number then you can skip to the square root of the negative integer but if you don't know anything about square root then don't worry because, in this lesson, we will teach you what is a square root and how to find the square root of an integer.

What is Square Root?

A square root is a number that you will get when the number is multiplied by itself. The symbol of the square root is \sqrt { }. For example, your teacher asks you to find the square root of 16. You will write like this \sqrt { 16 }. The condition of the square root is that the number should multiply itself which will result in 16 (because we are finding the square root of 16 here). If we multiply 4 by itself, we can get 16, let's check 4 \times 4 = 16. Hence, the square root of 16 is 4.

Q. Find the square root of 16

\sqrt { 16 }

\sqrt { { (4) }^{ 2 } }

4

A square root is the half-power of a number too. For example, we can write \sqrt { 16 } like this too { (16) }^{ \frac { 1 }{ 2 } }. When we take the square of any number, it multiplies with the power (which is \frac { 1 }{ 2 } since it already has a square root on it).

{ (16) }^{ \frac { 1 }{ 2 } }

{ ({ 4 }^{ 2 }) }^{ \frac { 1 }{ 2 } }

{ (4) }^{ \frac { 1 }{ 2 } \times 2 }

4

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Square Root of Positive Integer

Taking a square root of a positive integer is pretty simple. As a matter of fact, there is no twist here, it is the same as taking a square root of a number.

The square roots of integers have two signs: positive and negative.

\sqrt { 16 } = 4 \qquad { 4 }^{ 2 } = 16

\sqrt { 16 } = -4 \qquad { (-4) }^{ 2 } = 16

Square Root of Negative Integer

Although calculating the square root of a positive integer is easy but when calculating a negative integer there is a problem. Just a negative sign inside of a square root changes everything. The root of any negative integer can't be solved hence the answer will be impossible. A radicand is always a positive number or equal to zero because it is a square number.

\sqrt { 16 } = NP \qquad { (?) }^{ 2 } = -16

Even if we take the square of -4, it will result in positive 16 not negative 16 and that is why we call them imaginary numbers.

 

Algorithm of a Square Root,   Square Root of Decimal Numbers.

Square Root Worksheet.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.