Question

How do you simplify \[\sqrt {10} \]?

Answer 1

Hint: In this question, we need to simplify the square root of\[10\]. An operation that, when applied to a number, returns the value that when multiplied by itself gets the number given. We take the square root of the value to be positive because there are no real numbers that when multiplied together give you a negative number.

Complete step-by-step solution:
In the given question,
By solving the square root of \[10\], we get
We perform an operation that, we use a other method is to simplify the square root of the given number and then use the approximations of the prime numbers square roots
The square of given number \[10\] can be expressed as the following, we can get
\[\sqrt {10} = \sqrt {5 \times 2} \],
By simplify it, we get
\[\sqrt {10} = \sqrt 5 \cdot \sqrt 2 = 2.24 \times 1.41\], Since,\[\sqrt 5 = 2.24,\sqrt 2 = 1.41\]
Now, we get
\[\sqrt {10} = 3.16\]
Since, The Square root of \[\sqrt {10} = 3.16\]

Therefore, the simplification of the square root of \[\sqrt {10} \] is \[3.16\].

Additional information: We perform Addition, subtraction, multiplication, and division are the common operations on numbers in mathematics. However, some more advanced operations and manipulations are sometimes added to this list: square roots, exponentiation, logarithmic functions, and even trigonometric functions. Only the square root definition will be explained in this section.

Note: It is important to note, we use another approach to simplify the square root first and then use the approximations of the prime numbers square roots (typically rounded to two decimal places). The number you are taking the square root of must be positive because there are no real numbers that when multiplied together give you a negative number.