4th Root Calculator
Last Updated :
30 Dec, 2023
In the general nth root of a number is a number that is multiplied by itself n times. The 4th root of a number is an nth root number where n = 4 i.e., a number is multiplied by itself 4 times. The representation of an nth root of a number x is given as n√x.
4th Root of a number
The 4th 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 4th 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 4th root and we can take it out from the 4th root as a. i.e., 4√a4=a.
In the above sample example, 4th root and power 4 get canceled to each other.
Sample Problems
Question 1: Find 4th 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 4th 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 4th 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 4th root of 81.
Question 4: Find 4√4096?
Solution:
4√4096 = 4√(8 × 8 × 8 × 8)
= 8
So 4th root of 4096 is 8
Question 5: Find the 4th 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 4th root as 2. Like this, we can take any number with power as 4 from the 4th root.
Question 6: Find the 4th 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 4th root of 96 is 2 × 4√6
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