Answer
Verified
387.6k+ views
Hint:After reading the question carefully, first try to know what is the rationalising factor, then by converting the given surd into the simplest form, you can identify the simplest form of the rationalising factor of the given surd. So, follow the below step by step process to get a relevant explanation.
Complete step-by-step answer:
Surd: A surd is an expression that consists of square root, cube root or other root symbol. Surds are used to write irrational numbers precisely.
Rationalising factor: The factor of multiplication by which rationalization is taken, that factor is called as rationalizing factor. If the product of two irrational numbers or surds is a rational number, then each surd is a rationalizing factor for each other.
\[\sqrt {50} \] can be written in the simplest form,
\[ \Rightarrow \sqrt {25 \times 2} = 5\sqrt 2 \]
Because the square root of \[25\] is \[5\].
Now to find out the simplest form of rationalizing factor of given surd, multiply it with \[\sqrt 2 \].
\[ = 5\sqrt 2 \times \sqrt 2 \]
\[ = 5 \times 2\] (Since, \[\sqrt 2 \times \sqrt 2 = 2\])
\[ = 10\]
As \[10\] is a rational number, \[\sqrt 2 \] is a rationalizing factor for the given surd and it is also the simplest form.
Note:Make sure that the rationalizing factor that you find is in the simplest form if it is particularly mentioned in the question. The rationalizing factor that you find is perfectly correct only if it provides a rational number after multiplying the rationalizing factor with it. Be careful with the calculations. We can also observe that the product of two similar surds is always a rational number and they are rationalizing factors to each other though it may not be the simplest form.
Complete step-by-step answer:
Surd: A surd is an expression that consists of square root, cube root or other root symbol. Surds are used to write irrational numbers precisely.
Rationalising factor: The factor of multiplication by which rationalization is taken, that factor is called as rationalizing factor. If the product of two irrational numbers or surds is a rational number, then each surd is a rationalizing factor for each other.
\[\sqrt {50} \] can be written in the simplest form,
\[ \Rightarrow \sqrt {25 \times 2} = 5\sqrt 2 \]
Because the square root of \[25\] is \[5\].
Now to find out the simplest form of rationalizing factor of given surd, multiply it with \[\sqrt 2 \].
\[ = 5\sqrt 2 \times \sqrt 2 \]
\[ = 5 \times 2\] (Since, \[\sqrt 2 \times \sqrt 2 = 2\])
\[ = 10\]
As \[10\] is a rational number, \[\sqrt 2 \] is a rationalizing factor for the given surd and it is also the simplest form.
Note:Make sure that the rationalizing factor that you find is in the simplest form if it is particularly mentioned in the question. The rationalizing factor that you find is perfectly correct only if it provides a rational number after multiplying the rationalizing factor with it. Be careful with the calculations. We can also observe that the product of two similar surds is always a rational number and they are rationalizing factors to each other though it may not be the simplest form.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE