Simplify Square Root of 50 in Simplest Radical Form

The square root of 50 in the simplest radical form is 5√2. In this post, we will learn how to find the simplified radical form of root 50.

How to Simplify Root 50

To simplify the square root of 50 in simplest radical form, we need to follow the steps provided below.

Step 1: At first, we will factorise the number 50. Note that 50 is divisible by 2 and can be written as

50 = 2 × 25.

And 25 can be expressed as

25 = 5 × 5

Thus, 50 = 2 × 5 × 5 …(∗)

This is the prime factorization of 50.

Step 2: Now, taking square root on both sides of (∗), we get that

$\sqrt{50}$ $=\sqrt{2 \times 5 \times 5}$

= $\sqrt{2}$ × $\sqrt{5 \times 5}$

= √2 × 5 using the formula √(a×a) =a

= 5√2.

So 5√2 is the simplified radical form of the square root of 50. In other words,

√50 = 5√2.

Video Solution on How to Simplify Root 50:

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