# Square root of 32

To find the value of the square root of 32, we need to first understand the concept of square roots. We know that the square root of a number $x$ is denoted by $\sqrt{x}.$ So √32 is the square root of 32, and by definition, it is a number $x$ when multiplied by itself will be 32. Thus we need to find the number $x$ such that $x \times x=32.$

#### Overview of Square Root of 32

• The value of square root of 32 is 5.65686…
• Square root of 32 in radical form: √32
• Note that √32 is a quadratic surd.
• 321/2 is the exponential form of square root of 32
• Square root of 32 is irrational.
• √32=4√2
• Square root of 32 is 5.6569 up to 4 decimal.
• Square root of 32 is not a whole number.
• 32 is not a perfect square
• 32 square: 322 =32 × 32 =1024

#### Simplify Square Root of 32

What is the simplified radical form of square root of $32$?

Note that 32 = 16×2.

So $\sqrt{32}$ $=\sqrt{16 \times 2}$

$=\sqrt{16} \times \sqrt{2}$ $[\because \sqrt{x \times y}=\sqrt{x} \times \sqrt{y}]$

As $\sqrt{16}=4,$ we obtain that

$\sqrt{32}$$=4 \times \sqrt{2}$ $=4\sqrt{2}.$

4√2 is the simplified form of square root of 32.

#### Value of Square Root of 32

Simplifying the surd $\sqrt{32},$ we will get the value of square root of $32.$ From above we get that $\sqrt{32}$ $=4 \times \sqrt{2}.$  We know that $\sqrt{2}=1.414.$ Putting this value, we have

$\sqrt{32}=4 \times 1.414$

$=5.656$

So the value of square root of $32$ is $=5.656.$

#### Is Square Root of 32 Rational?

We know that the square root of 32 is 4√2, that is, √32=4√2.

As √2 is an irrational number, we conclude that 4√2 is not a rational number.

∴ The square root of 32 is also an irrational number.

So √32 is not a rational number.

#### Square Root of 32 by Prime Factorization

At first, we will try to find the prime factorization of $32.$ As $32$ is an even number, $2$ will divide it. So we have

$32=2 \times 16.$

In a similar way, $16=2 \times 8.$

As $8=2 \times 4$ and $4=2 \times 2,$ we finally get that

$32=2 \times 2 \times 2 \times 2 \times 2$ $\cdots (\star)$

As $2$ is a prime number, the above is the prime factorization of $32.$ Now we will take square root on both sides of $(\star)$, and doing that we get

32=(2×2×2×2×2)

=(2×2) ×(2×2) ×2 as we know that √(x×y×z)=√x ×y ×z. Here x=2×2, y=2×2 and z=2

= 2 × 2 ×2

= 42

Thus, the square root of 32 is 42 obtained by the prime factorization method.