Question

How do you write $ \sqrt {160} $ in simplified radical form?

Answer 1

Hint: We will start by factorising the term inside the square root. Then we will separate all the like terms and all the alike terms. Then we will check if any squares are present, if present then we will take those terms out of the square root.

Complete step-by-step answer:
First we will start off by forming factors.
 $
   = \sqrt {160} \\
   = \sqrt {(16 \times 10)} \\
   = \sqrt {(4 \times 4 \times 10)} \\
   = \sqrt {(2 \times 2 \times 2 \times 2 \times 2 \times 5)} \;
  $
Now we separate the like terms.
 $ = \sqrt {{2^5} \times 5} $
Now we check if any square root is present to take them out of the square root.
\[
   = \sqrt {{2^4} \times 2 \times 5} \\
   = \sqrt {{{\left( {{2^2}} \right)}^2} \times 2 \times 5} \\
   = 4\sqrt {10} \;
 \]
So, $ \sqrt {160} $ in simplified form is written as $ 4\sqrt {10} $ .
So, the correct answer is “ $ 4\sqrt {10} $ ”.

Note: While factorising the terms, factorise until you cannot factorise any further. Also, while factorising take into consideration the signs of the terms. While searching for square roots, searching for even powers, it makes the process easier.