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Rationalize the denominator of each of the following:
For rationalizing the denominator, multiply both numerator and denominator with √5
For rationalizing the denominator, multiply both numerator and denominator with √12
For rationalizing the denominator, multiply both numerator and denominator with √3
For rationalizing the denominator, multiply both numerator and denominator with √2
For rationalizing the denominator, multiply both numerator and denominator with
Find the value to three places of decimals of each of the following. It is given that
Given,
Rationalizing the denominator by multiplying both numerator and denominator with
Rationalizing the denominator by multiplying both numerator and denominator with √10
Rationalizing the denominator by multiplying both numerator and denominator with √2
Rationalizing the denominator by multiplying both numerator and denominator with√5
Express each one of the following with rational denominator:
Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor
As we know,
As we know, (a + b) (a - b) = (a2 - b2)
As we know, (a - b)2 = (a2 – 2 × a × b + b2)
As we know, (a + b)(a - b) = (a2 - b2)
Rationalize the denominator and simplify:
Simplify:
Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factorand the rationalizing factor
Now, (a + b)(a - b) = (a2 - b2)
Now as we know, (a + b)(a - b)
Now as we know, (a + b)(a - b) = (a2 - b2)
Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factorthe rationalizing factorand the rationalizing factor
Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor the rationalizing factorand the rationalizing factor
Since, (a + b) (a - b) = (a2 - b2)
In each of the following determine rational numbers a and b:
On comparing the rational and irrational parts of the above equation, we get, a = 2 and b = 1
As we know, (a + b)(a - b)= (a2 - b2)
On comparing the rational and irrational parts of the above equation, we get, a = 3 and b = 2
On comparing the rational and irrational parts of the above equation, we get,
On comparing the rational and irrational parts of the above equation, we get, a = -1 and b = 1
On comparing the rational and irrational parts of the above equation, we get, a = 92 and b = 12
If x = 2+√3, find the value of
Given, x = 2 + √3,
To find the value of
We have, x = 2 + √3,
We know that, (a3 + b3) = (a + b)(a2 − ab + b2)
Putting the value of x+1x in the above equation, we get,
If x = 3+√8, find the value of
Given, x = 3 + √8,
We have, x = 3 + √8,
Find the value of it being given that √3 = 1.732 and √5 = 2.236.
= 3(2.236 + 1.732) = 3(3.968) = 11.904
Find the values of each of the following correct to three places of decimals, it being given that
= 7 + 7.07 = 14.07
Iffind the value of 4x3 + 2x2- 8x + 7.
Given,and given to find the value of 4x3 + 2x2 − 8x + 7
2x = √3 + 1
2x – 1 = √3
Now, squaring on both the sides, we get, (2x − 1)2 = 3
4x2 − 4x + 1 = 3
4x2 − 4x + 1 − 3 = 0
4x2 − 4x − 2 = 0
2x2 − 2x − 1 = 0
Now taking 4x3 + 2x2 − 8x + 7
2x(2x2 − 2x − 1) + 4x2 + 2x + 2x2 − 8x + 7
2x(2x2 − 2x − 1) + 6x2 − 6x + 7
As, 2x2 − 2x − 1 = 0
2x(0) + 3(2x2 − 2x − 1)) + 7 + 3
0 + 3(0) + 10
10
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Chapter 3: Rationalisation Exercise – 3.1...