5th Root Calculator

The number system concerns distinct types of numerals such as prime numerals, odd numerals, even numerals, rational numerals, whole numerals, etc. These numerals can be represented in the state of realities as well as terms properly. For instance, the integers like 20 and 25 illustrated in the formation of figures can also be reported as twenty and twenty-five. A Number system or numeral system is described as an uncomplicated/easy system to display numerals and formations. It is a unique form of displaying numerals in math and arithmetic forms.

Numbers

Numbers are used in different arithmetic significance suitable to give various arithmetic operating like addition, subtraction, multiplication, etc., which are suitable in daily lives for the reason of calculation. The value of a numeral is selected by the digit, its place value in the numeral, and the frame of the number system. Numbers usually are also known as numerals are the numerical values used for counting, measurements, setting, and computing elemental excesses. Numerals are the formations used for the reason of counting or estimating numerals. It is formed by numerals such as 4, 5, 78, etc.

What is a fifth root?

The fifth root of a numeral is the digit that would have to be multiplied by itself by 5 bits to get the actual digit. For instance, the fifth root of 32 is 2 as 2 × 2 × 2 × 2 × 2 is 32. The fifth root of 3125 is 5, as 5 × 5 × 5 × 5 × 5 is 3125.

How to calculate the fifth root

Even for ideal fifth root numerals, the fifth root can be hard to compute by hand. The most fundamental methods apply trial and error.

Example:

Find the fifth root of 7776

1. Try a number – 4 : 4 x 4 x 4 x 4 x 4 = 1024 (too low)
2. Try another number that is more than 4 – 5 : 5 x 5 x 5 x 5 x 5 = 3125(too low)
3. Try a number that is more than 5 – 8 – 8 x 8 x 8 x 8 x 8 = 32768 (too high)
4. Try a number in between 5 and 8 – 6 – 6 x 6 x 6 x 6 x 6 = 7776 (answer)

A fifth root can also be calculated as a similar numeral to the exponent 1/5.

⁵√number = number^1/5

Find the 5th root of…	5th root
5√1	= 1.0000000000
5√2	= 1.1486983550
5√3	= 1.2457309396
5√4	= 1.3195079108
5√5	= 1.3797296615
5√6	= 1.4309690811
5√7	= 1.4757731616
5√8	= 1.5157165665
5√9	= 1.5518455739
5√10	= 1.5848931925

Sample Problems 

Problem 1: Calculate the 5th root of a rational number -1024/243.

Solution:

⁵√-1024/243

= ⁵√-1024 / ⁵√243

= -4/3

Problem 2: Calculate 5th root of an expression 32y¹⁰

Solution:

⁵√32y¹⁰ 

we can solve 32 by using 

a^m=b

m√b=a

So, we get ⁵√(2)⁵y¹⁰

Now we can solve y¹⁰ by using 

a^m×aⁿ=a^m+n

(a^m)ⁿ = a^mn

So, we get ⁵√(2)⁵(y²)⁵

cancel all the ⁵ we get

= 2y²

Problem 3: Calculate the 5th root of 32.

Solution:

= ⁵√32

= 32^1/5

= (2⁵)^1/5

= 2^5×1/5

= 2

Problem 4: Calculate the 5th root of 243.

Solution:

= ⁵√243

= 243^1/5

= (3⁵)^1/5 

= 3

Problem 5: Calculate the 5th root of 1024/3125.

Solution:

= ⁵√1024/3125

= (1024/3125)^1/5

= ((4/5)⁵)^1/5

= 4/5