√2/1-√2
rationalize the dinominator
Answers
Step-by-step explanation:
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Step-by-step explanation:
Given:-
√2/(1 - √2)
To find out:-
Rationalised value of denominator.
Solution:-
We have,
√2/(1 - √2)
The denomination is 1 - √2.
We know that
The rationalising factor of a-√b = a+√b.
So, the rationalising factor of 1-√2 = 1+√2.
On rationalising the denominator them
→ [√2/(1 - √2)] × [(1 + √2)/(1+√2)]
→ [√2(1+√2)]/[(1 - √2)(1 + √2)
Now, Consider the denominator (1 -√2)(1+√2). Multiplication can be transformed into different of square using algebraic Identity:
(a - b)(a+b) = a^2 - b^2
Where, we have to put in our expression a = 1 and b = √2 , we get
→ [√2(1+√2)]/[(1)^2 - (√2)^2]
Square 1 = 1. square √2 = 2 convert in denominator
→ [√2(1+√2)]/(1 - 2)
In denominator subtract 2 from 1 to get -1.
→ √2(1+√2)/-1
Anything divided by -1 gives it opposite
→ -√2(1+√2)
Use the distribution property to multiply √2 by 1+√2
→ -(√2(√2)^2)
The square of √2 is 2.
To find the opposite√2+2, find the opposite of each term.
→ -√2-2
Hence, the denominator is rationalised.
Answer:-
-√2-2
Used formulae:-
The rationalising factor of a-√b = a+√b.
(a - b)(a+b) = a^2 - b^2