# 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.
• 161/2 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

= 42×1/2  as we know that (am)n=am×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.

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