Question

How do you simplify: ${\text{Square root 40?}}$

Answer 1

Hint: For finding the square root of a given number, firstly we will simplify the expression of the square root of 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 are prime numbers. Combine factors using exponents. Then move bases outside of the square root if possible. Then the 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 $40$ . Square root of $40$ , can be written as $\sqrt {40} $.
Firstly, we find the two numbers, when it multiplied we get $40$. $2{\text{ and }}20$ is two numbers, it multiplied we get $40$. So, we can write$\sqrt {40} = \sqrt {2 \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 the Prime Number.
So, $20$ can write as, $20 = 2 \times 2 \times 5$
Step3: Then the repeated factors can be rewritten more efficiently by using exponents.
Therefore, $\sqrt {40} = \sqrt {2 \times {{\left( 2 \right)}^2} \times 5} $
Step4: Further, we can give the underneath root symbol the each of factor (number)
Therefore, $\sqrt {40} = \sqrt 2 \times \sqrt {{{\left( 2 \right)}^2}} \times \sqrt 5 $
After solving we get $\sqrt {40} = \sqrt 2 \times 2 \times \sqrt 5 $
We know that the $\sqrt 2 $ is approximately $1.41$ and $\sqrt 5 $is approximately $2.24$
Therefore \[\sqrt {40} = {\text{ }}1.41 \times 2 \times 22.24{\text{ }} \Rightarrow {\text{ }}6.3168{\text{ }}\]
Hence, $\sqrt {40} = {\text{ }}6.3168$.

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 areas on the integral part of the number in the usual manner.