Question

How do you simplify \[{20^{\dfrac{1}{2}}} \times {20^{\dfrac{1}{2}}}\] ?

Answer 1

Hint: We can write the problem as \[{20^{\dfrac{1}{2}}}{.20^{\dfrac{1}{2}}} = \sqrt {20} .\sqrt {20} \] . Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\] . Here we can see that 20 is not a perfect square. To solve this we factorize the given number.

Complete step-by-step answer:
Here we have multiplication of two square roots,
Given,
 \[\sqrt {20} \times \sqrt {20} \]
Since we can multiply the numbers within the radical symbol.
 \[ = \sqrt {20 \times 20} \]
 \[ = \sqrt {{{20}^2}} \]
Here square and square root will get cancels out we will have
 \[ = 20\] . Is the required answer.
So, the correct answer is “20”.

Note: If we have multiplication of two different exponents this method will not be applied. If we have \[\sqrt[3] {a}\] we can write it as \[{a^{\dfrac{1}{3}}}\] . If we have \[\sqrt[3] {a} \times \sqrt[2] {a}\] this can be written as \[{a^{\dfrac{1}{3}}} \times {a^{\dfrac{1}{2}}}\] . Since we have same base we can add the exponent \[{a^{\dfrac{1}{3} + \dfrac{1}{2}}} = {a^{\dfrac{5}{6}}}\] . We can solve this by multiplying ‘a’ five times and taking the sixth root of that number.