Note that the square root of a number $x$ is written as $\sqrt{x}.$ So we can express the square root of 16 as √16. In this section, we will learn how to find the square root of 16. But before we begin, let us note down the key things about the square root of sixteen.

- The square root of 16 is equal to 4. So √16=4.
- As square root of 16 is a whole number, 16 is a perfect square.
- The square root of 16 is a rational number.
- 16
^{1/2}is the exponential form of square root of 16. - √16 is the radical/surd form of square root of 16.
- The square root of 16 is 4.000 in decimal form.

Table of Contents

**What is the square root of 16?**

The square root of 16 is 4. To prove this, we will first find the factors of $16$ which are perfect squares. Observe that 16=4×4=4^{2}.

∴ √16=√(4^{2})

As square root is same as the power 1/2, we have

√16=(4^{2})^{1/2}

= 4^{2×1/2 } as we know that (a^{m})^{n}=a^{m×n}

= 4^{1}

= 4

So the value of the square root of 16 is equal to 4.

**Square Root of 16 by Prime Factorization**

We have now learned that the square root of $16$ is $4.$ Here we will find the same by prime factorization method. Firstly, we will factorize $16.$ As $16$ is an even number, it will be divisible by $2.$ So we can write $16=2 \times 8.$

Now, we will factorize the number $8.$ Again since $8$ is an even number, we have $8=2 \times 4.$ And we all know that $4=2 \times 2.$ Thus combining all the above factorizations, we obtain the prime factorization of $16$ which is given below:

\[16=2 \times 2 \times 2 \times 2.\]

Taking square root on both sides, we get that

$\sqrt{16}=\sqrt{2 \times 2 \times 2 \times 2}$

$=\sqrt{2 \times 2} \times \sqrt{2 \times 2}$ $[ \because \sqrt{x \times y}=\sqrt{x} \times \sqrt{y}]$

$=2 \times 2$ $[ \because \sqrt{a \times a}=a]$

$=4$

So $4$ is the square root of $16.$

**Is the square root of 16 rational?**

To answer the question let us recall the definition of a rational number. A number $x$ is said to be a rational number, if we can express $x$ as $\frac{p}{q}$ for some integers $p$ and $q$ with $q \neq 0.$

We know that $\sqrt{16}=\sqrt{4^2}$ $=\pm 4.$ Note that $+4=\frac{4}{1}$ and $-4=\frac{-4}{1}.$ Thus, both $+4$ and $-4$ are rational numbers. Hence, we conclude that the square root of $16$ is a rational number.

**Is 16 a perfect square? **

We have computed above that the square root of 16 is 4. Since 4 is a whole number, we can conclude that 16 is a perfect square number.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.