Question

What is \[4\] square root of \[80\]?

Answer 1

Hint:For finding the square root of a given number that is \[4\sqrt{80}\], we separate the terms \[4\]and \[80\]. And firstly, we find the square root of \[80\]. To do that we need to simplify the \[\sqrt{80}\], we will write \[80\] as \[4\]and \[20\], finding out the factors until we have all prime numbers. After getting the simplified answer of \[\sqrt{80}\] , we multiply the left out number \[4\]to the answer of \[\sqrt{80}\]. Then we get the resultant answer.

Complete step-by-step solution:
Let us solve the given question
We need to find the \[4\]square root of \[80\] .
\[4\]square root of \[80\]can be written as \[4\sqrt{80}\].
Let us take the square root of \[80\] that is \[\left( \sqrt{80} \right)\], firstly we find the number, when it multiplied, we get \[80\].
\[4\]and \[20\]are the two numbers and when multiplied we get \[80\].
So, we can write \[\sqrt{80}=\sqrt{4\times 20}\]
Next, we find the prime factors of \[4\]and \[20\], we will find the factors until the only factors are left with prime numbers.
So \[4\]can write as \[4=2\times 2\] and \[20\] can write as \[20=2\times 2\times 5\]
By using exponents, we can be rewritten the repeated factors
Therefore,\[\sqrt{80}=\sqrt{2\times 2\times 2\times 2\times 5}\Rightarrow \sqrt{{{\left( 2 \right)}^{4}}\times 5}\]
After simplifying, we get \[\sqrt{80}=\sqrt{{{\left( 2 \right)}^{4}}}\times \sqrt{5}\]
Which can also be written as \[\sqrt{80}={{\left( 2 \right)}^{2}}\times \sqrt{5}\]
Finally, we are multiplying left out number\[4\]to the \[\left( \sqrt{80} \right)\] , we get
\[4\sqrt{80}=4\times 4\times \sqrt{5}\]
\[\therefore 4\sqrt{80}=16\sqrt{5}\]
We know that the value of \[\sqrt{5}\]is approximately \[2.24\]
\[\therefore 4\sqrt{80}=16\times 2.24=35.84\]
Hence the value of \[4\sqrt{80}\]is either \[16\sqrt{5}\]or \[35.84\].

Note: Square root is the inverse option of squaring the positive square root of a number is denoted by the symbol \[\sqrt{{}}\]. While solving for the square root of the number, we should take utter concentration.