Question

How do you find the square root of \[80\] ?

Answer 1

Hint: For finding the square root of a given number, firstly we will simplify the expression of the square root of the given number involving finding factors. This means we are trying to find the two whole numbers that, when we multiplied, we get the number .Then continue factoring until you have all prime numbers .To simplify a number underneath the square root symbol, It is very useful to keep factoring the factors unit. The only factors that are left prime number combine factors using exponents. Then move bases outside of square root if possible, Then rule for moving bases outside of the symbol is to divide the exponent power 2.

Complete step-by-step answer:
Step1: We find the square root of \[80\]. Square root of \[80\] can written as \[\sqrt {80} \]
Firstly, we find the number, when it multiplied we get \[80\]. \[4\]and \[20\] is two numbers and when multiplied we get \[80\]. So, we can write \[\sqrt {80} = \sqrt {4 \times 20} \]
Step2: Further find the prime number (factors) because it is very useful to keep factoring the factors until the only factors that are left are prime numbers.
So 4 can write as \[4{\text{ }} = {\text{ }}2 \times 2\] and \[20\] can write as \[20 = 2 \times 2 \times 5\]
Step3: Then the repeated factors can be rewritten more efficiently by using exponents.
Step4: Further, we can give the underneath root symbol, each of factor (number).
Therefore, \[\sqrt {80} = \sqrt {2 \times 2 \times 2 \times 2 \times 5} = \sqrt {{{\left( 2 \right)}^4} \times 5} \]
After solving, we get \[\sqrt {80} = \sqrt {{{\left( 2 \right)}^4}} \times \sqrt 5 \]
That we can write as \[\sqrt {80} = {\left( 2 \right)^2} \times \sqrt 5 \]
We know that the \[\sqrt 5 \] is approximately \[2.24\]
Therefore \[\sqrt {80} = 4 \times 2.24 = 8.96\]
Hence \[\sqrt {80} = 8.96\]

Note: Square root is the inverse option of squaring the positive square root of a number is denoted by the symbol \[\sqrt {} \]. Example \[\sqrt {9 = 3} \] to find the square root of a decimal number .We put bars on the integral part of the number in the usual manner.