Question

What is the simplified square root of $ 845 $ in simplified radical form?

Answer 1

Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example $ 5*5 = 25 $ , here square root of $ 25 $ is $ 5 $ . There is no such formula to calculate square root formula but two ways are generally considered. They are a prime factorization method and division method. The symbol $ \sqrt {} $ is used to denote square roots and this symbol of square roots is also known as radical. So we have to write the value in this radical form.

Complete step by step solution:
Here we have $ 845 $ .
To find the square root of the number we write the number in the product of all the prime factors associated with it.
We can find the value of the number by the prime factorisation method. So we can write $ 845 = 5 \times 13 \times 13 $ .
So by substituting $ 845 $ with these factors under square root we have $ \sqrt {5 \times 13 \times 13} $ .
It gives the value $ 13\sqrt 5 $ .
Hence the radical form of $ 845 $ is $ 13\sqrt 5 $ .
So, the correct answer is “ $ 13\sqrt 5 $ ”.

Note: We should note that if $ b = a \times a $ , then it is the square root of $ b $ i.e. $ \sqrt b = \sqrt {a \times a} $ , which is equal to $ a $ . The number written inside the square root symbol or radical is known as radicand. We know that all real numbers have two square roots, one is a positive square root and another one is a negative square root. The positive square root is also referred to as the principal square root.