4th Root Calculator

In the general n^th root of a number is a number that is multiplied by itself n times. The 4^th root of a number is an n^th root number where n = 4 i.e., a number is multiplied by itself 4 times. The representation of an n^th root of a number x is given as ⁿ√x.

4^th Root of a number

The 4^th Root of a number is a number when multiplied four times by itself, then the result obtained will be the original number. We can also call it a double square root because 4^th root of a number is the square root of a number. Let’s move into an exam to get more understanding.

Any number which is having the power of 4 can be taken out of the 4th root. For example, a⁴ is a number in the 4^th root and we can take it out from the 4^th root as a. i.e., ⁴√a⁴=a. 

In the above sample example, 4^th root and power 4 get canceled to each other.

Sample Problems

Question 1: Find 4^th root of 16

Solution:

When 2 is multiplied 4 times by itself we get 16.

i.e., 2⁴ = 2 × 2 × 2 × 2 = 16

So 2 is the 4^th root of 16.

Question 2: Find ⁴√256 

Solution:

⁴√256 = ⁴√(4 × 4 × 4 × 4)

= 4

So 4th root of 256 is 4

Question 3: Find 4^th root of 81

Solution:

When 3 is multiplied 4 times by itself we get 81.

i.e., 3⁴ = 3 × 3 × 3 × 3 = 81

So 3 is 4^th root of 81.

Question 4: Find ⁴√4096?

Solution:

⁴√4096 = ⁴√(8 × 8 × 8 × 8)

= 8

So 4^th root of 4096 is 8

Question 5: Find the 4^th root of 48

Solution:

48 can be written as 2 × 2 × 2 × 2 × 3

⁴√48 = ⁴√(2 × 2 × 2 × 2 × 3)

= ⁴√(2⁴ × 3)

= 2 × ⁴√3

So, ⁴√48 = 2 × ⁴√3

In this problem 2 to the power of 4 is taken out from the 4^th root as 2. Like this, we can take any number with power as 4 from the 4^th root.

Question 6: Find the 4^th root of number 32?

Solution:

⁴√32 = ⁴√(2 × 2 × 2 × 2 × 2)

= ⁴√(2⁴ × 2)

= 2 × ⁴√2

So, ⁴√32 = 2 × ⁴√2

Question 7: what is the result of ⁴√96.

Solution:

⁴√96 = ⁴√(2 × 2 × 2 × 2 × 2 × 3)

= ⁴√(2⁵ × 3)

= ⁴√(2⁴ × 2 × 3)

= 2 × ⁴√(2 × 3)

= 2 × ⁴√6

Hence 4^th root of 96 is 2 × ⁴√6