Question

How do you find the square root of \[32\]?

Answer 1

Hint: For find the square root of given number, Firstly we will simplifying the expression of the square root of given number involves finding factors this means we are trying to find the two whole number 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:
 step 1: We find the square root of \[32\] square root of \[32\] we can written as \[\sqrt {32} \] firstly, We find the two number which it multiplied we get \[32\] \[,{\text{ }}2\] and \[16\] is two number ,if multiplies we get \[32\]. So we can write \[\sqrt {32} \]
\[ = \sqrt {2 \times 16} \]
Step 2: 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, \[16\] can write, \[16 = 2 \times 2 \times 2 \times 2\]
So, we can write as \[\sqrt {32} = \sqrt {2 \times 2 \times 2 \times 2} \]
Step3: Then the reciprocal factors can be rewritten more efficiently by using exponents
Therefore,\[\sqrt {32} = \sqrt 2 \times \sqrt {{{\left( 2 \right)}^4}} \]
Step4: Further we can give the underneath root symbol, the each of number
Therefore, \[\sqrt {32} = \sqrt 2 \times \sqrt {{{\left( 2 \right)}^4}} \]
After solving we get \[\sqrt {32} = \sqrt 2 \times {\left( 2 \right)^2}\]
We know that the \[\sqrt 2 \] is approximately \[1.41\]
So, \[\sqrt {32} = 1.41 \times {\left( 2 \right)^2}\]
Hence, \[\sqrt {32} \]\[ = 5.64\]

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.