Question

How do you simplify $ \sqrt {87} $ ?

Answer 1

Hint: In this question we need to simplify $ \sqrt {87} $ . We will break the number into the roots as the product of the number, and then if the product contains two copies of the same factors, where we can write the factor to the exponent of two. Here, the product raised to the power rule is applied, and then we will take the number out from the root. Then, that will be our simplified form. If we cannot find any pairs of common factors, then the given number is its simplified term.

Complete step-by-step answer:
To simplify a square root, we need to make the number inside the square root as small as possible. We take out anything that is a perfect square, that is, we factor inside the radical symbol and then take out in front of that symbol anything that has two copies of the same factor.
Now, let’s try to simplify $ \sqrt {87} $ ,
 $ \sqrt {87} = \sqrt {3 \times 29} $
Here, we don’t have two copies of the same factor.
When we can’t simplify a number to remove a square root then, it is a surd. The surds have a decimal which goes on forever without repeating, and are irrational numbers. An irrational number is a real number that cannot be written as a simplest fraction. The surd is used to be another name for ‘irrational’, but it is now used for a root that is irrational. Thus, we can say that when it is a root and irrational, it is a surd. But not all roots are sure.
Therefore, we cannot further simplify $ \sqrt {87} $ .
So, the correct answer is “ $ \sqrt {3 \times 29} $ ”.

Note: The symbol for the square root is called a radical symbol which looks like “ $ \sqrt {} $ ”. This expression is read as “the square-root” or “radical”. The number written under the radical symbol is called the radicand. The square root symbol always means to find the positive root, called principal root. Exponents and roots are connected because roots can be expressed as fractional exponents.