Question

How do you multiply \[\sqrt { - 20} \times \sqrt { - 5} \] ?

Answer 1

Hint: Here the given question based on the Multiplication and Division of Radicals, we have to multiply the given radicals. First, we should write the radical in exponent form like \[\sqrt x = {x^{\dfrac{1}{2}}}\] after to multiply use the one of the rule of exponent i.e., \[\sqrt a \times \sqrt b = \sqrt {ab} \] and on further simplification we get the required solution.

Complete step by step solution:
The square root of a natural number is a value, which can be written in the form of \[y = \sqrt a \] . It means ‘y’ is equal to the square root of a, where ‘a’ is any natural number. We can also express it as \[{y^2} = a\] .Thus, it is concluded here that square root is a value which when multiplied by itself gives the original number, i.e., \[a = y \times y\] .
The symbol or sign to represent a square root is ‘ \[\sqrt {} \] ’. This symbol is also called a radical. Also, the number under the root is called a radicand.
Consider the given expression \[\sqrt { - 20} \times \sqrt { - 5} \]
Now multiply the radicands using the power of exponent \[\sqrt a \times \sqrt b = \sqrt {ab} \]
Where a=-20 and b=-5
 \[ \Rightarrow \sqrt { - 20 \times - 5} \]
On multiplying, the number inside the radicand and using the sign conversion
\[ - \times - = + \] , then
 \[ \Rightarrow \sqrt {100} \]
As we know, 100 is the square number of 10, then
 \[ \Rightarrow \sqrt {{{10}^2}} \]
On cancelling square and root, we get
 \[ \Rightarrow 10\]
Hence, the required solution is 10.
So, the correct answer is “10”.

Note: The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\] , where a is the numeral and n represents the number of times the number is multiplied. For the exponential numbers we have a law of indices and by applying it we can solve the given number.