Question

What is the square root of \[8\] (squared) ?

Answer 1

Hint: We have to find the square root of \[8\] . We solve this question by resolving the value \[8\] into its prime factors . The square root of a number is represented as the value of another number when it is multiplied by itself gives the value of as the original number . After finding the prime factors we can calculate the value of a square root . If a prime factor is left single or in odd factor terms then we can calculate it using the table method of square root .

Complete step-by-step solution:
Given : we have to find the value of \[\sqrt 8 \]
To find the square root using prime factorisation method , we resolve the original number into prime factors
So , prime factors of 8 in table form
\[8 = 2 \times 4\]
\[4 = 2 \times 2\]
\[2 = 2 \times 1\]
Hence the prime factors of \[8\] are \[2\] , \[2\] , \[2\] .
As \[8\] has a factor of \[2\] three times , so
In the value of square root it will give only one \[2\]
\[8 = {2^2} \times 2\]
Square root of \[8 = 2\sqrt 2 \]
Now , we have to find the square root of \[2\]
Also , we know
\[\sqrt 2 = 1.41421\]
Now ,
\[\sqrt 8 = 2 \times 1.41421\]
\[\sqrt 8 = 2.82842\]
Thus , \[\text{The square root of 8} = {\text{ }}2.82842\]

Note: A square root number can be a rational or irrational number . If the square root of a number can be represented in terms of natural numbers then it is a rational number i.e. it can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\] . And if square root of a number cannot be represented in terms of natural number than it is an irrational number i.e. it can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\] .