# Square Root of 50: Simplified Radical Form

The simplified radical form of square root 50 is 5√2, that is, √50 = 5√2. The value of root 50 is equal to 7.071. As the square root of a number x is denoted by √x, root 50 is written as √50. Here, we will learn how to calculate the square root of 50. Note that

• √50 = 7.071
• 501/2 is the exponential form of square root of 50.
• √50 is the radical form of square root of 50.
• The square root of 50 is 7.071 corrected up to 3 decimal places.
• 50 is not a perfect square.
• Square of 50: 50×50 = 2,500
• √50 is a quadratic surd.
• The simplified form of √50 is 5√2.

## Simplify square root of 50?

To find the square root of 50 in simplest radical form, let us express 50 as a product of perfect squares or as a product of a perfect square and a non-perfect square.

We can write 50 as

50= 25×2,

where 25 is a perfect square number as 25=52 and 2 is a non-perfect square. Now, taking square root on both sides of 50= 25×2, we get that

√50 = √(25×2)

= √25 × √2 using the rule √(a×b) = √a × √b.

= 5√2

So the simplest radical form of root 50 is equal to 5√2.

Square root of 32: The square root of 32 is 4√2.

Square root of 108: The square root of 108 is 6√3.

Square root of 117: The square root of 117 is 3√13.

## Is 50 a perfect square number?

Note that √50=5√2.

As √2 is not an integer, so 5√2 cannot be an integer as well. This shows that 50 is not a perfect square number.

The number 50 is a non-perfect square number.

Hence, √50 is a quadratic surd.

## Is Square root of 50 Rational?

As √50=5√2 and √2 is an irrational number,  so the square root of 50 is an irrational number.

Thus, we conclude that √50 is an irrational number.

## What is the value of root 50?

The simplest radical form of square root of 50 is given by

√50 = 5√2.

As the value of √2 is 1.414, the value of root 50 will be equal to

√50 = 5√2 = 5 × 1.414 = 7.07

Thus the value of the square root of 50 is 7.07.

## Square root of 50 by Prime Factorization

We need to factorize the number 50 in order to find the square root of 50 by the prime factorization method.

As 50 is an even number, it will be divisible by 2. Hence, we can write

50=2×25 …(I)

Now, factorize the number 25. Note that 25 is a perfect square of 5, that is,

25=5×5 …(II)

Combining (I) and (II) we obtain the prime factorization of 50 which is given below.

50=2×5×5

Taking square root on both sides of the above, we get that

√50 = $\sqrt{2 \times 5 \times 5}$

= √2 × √(5×5)

= √2 × 5 using the rule √(a×a) = a.

= 5√2

So 5√2 is the value of the square root of 50.

## FAQs on Square Root of 50

Q1: What is square root of 50 in radical form?

Answer: The square root of 50 in radical form is given by √50=5√2.

Q2: Is root 50 a quadratic surd?