Question

The value of \[\sqrt {20} \times \sqrt 5 \] is
A) \[10\]
B) \[2\sqrt 5 \]
C) \[20\sqrt 5 \]
D) \[4\sqrt 5 \]

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.
\[ \Rightarrow \,\,\,\,\sqrt {100} \]
As we know, 100 is the square number of 10, then
\[ \Rightarrow \,\,\,\,\sqrt {{{10}^2}} \]
On cancelling square and root, we get
\[ \Rightarrow \,\,\,\,10\]

Therefore, the value of \[\sqrt {20} \times \sqrt 5 \] is $10$. So, option (A) is correct.

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.