[Solved] What is Fourth Root of 625

The fourth root of 625 is equal to 5 and it is written as follows ∜625 =5. In this post, we will learn how to find the fourth root of 625.

4th root of 625 formula is given as follows:

∜625 = 5,

where

• √ denotes the radical symbol (or square root)
• ∜ is used to mean the fourth root.

How to Find the Fourth Root of 625

To find the 4th root of 625, first, we need to write the prime factorization of 625. As 625 has the last digit 5, it will be divisible by 5, and we get that

625 ÷ ${\color{red}5}$ =125.

Next, we need to factorize 125. As it has the last digit 5, so we will divide 125 by 5.

125 ÷ ${\color{red}5}$ =25.

And, 25 ÷ ${\color{red}5}$ = 5

5 ÷ ${\color{red}5}$ =1.

Thus, 625 will be the product of red-colored numbers and we have:

625 = 5 × 5 × 5 × 5

∴ 625 = 5⁴

Taking the fourth root on both sides, we get that

∜625 = ∜5⁴

⇒ ∜625 = $5^{4 \times \frac{1}{4}}$ by the rule $\sqrt[n]{a^m}=a^{mn}$.

⇒ ∜625 = 5¹ = 5.

So the fourth root of 625 is equal to 5.

Note: We know that if x is a fourth root, then -x is also a fourth root, which means both 5 and -5 are the fourth roots of 625. That is,

∜625 = 5, -5.

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