Square root of 16

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.

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=4². 

∴ √16=√(4²)

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

√16=(4²)^1/2

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

= 4¹

= 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.